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Aly R Seadawy - One of the best experts on this subject based on the ideXlab platform.
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construction of soliton solutions of the modify unstable nonlinear schrodinger Dynamical Equation in fiber optics
Indian Journal of Physics, 2020Co-Authors: Aly R Seadawy, Mujahid IqbalAbstract:In this research article, we investigated the universal model of integrable system of modify unstable nonlinear Schrodinger Equation. The mUNLSE described the disturbance of time period in slightly stable and unstable media and managed the instability of modulation wave train. We found the exact and solitary wave solutions of mUNLSE with the help of modified extended auxiliary Equation mapping method. As a result, exact and solitary wave solutions in the form of elliptic functions, trigonometric functions, hyperbolic functions, bright and dark solitons, traveling wave, kink-type solitons and periodic solitary wave solution are obtained. These solutions show the power and effectiveness of this new method and two- and three-dimensional graphically with the help of computer software Mathematica. We can also solve other unstable nonlinear system of PDEs which are involved in Mathematical physics and many other branches of physical sciences with the help of this new method.
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propagation of long internal waves in density stratified ocean for the 2 1 dimensional nonlinear nizhnik novikov vesselov Dynamical Equation
Results in physics, 2020Co-Authors: Mujahid Iqbal, Aly R Seadawy, O H KhalilAbstract:Abstract Our aim in this article to constructed the new solitary wave solutions of (2+1)-dim nonlinear Nizhnik-Novikov-Vesselov Equation by novel approach which is extended modified rational expansion method. The new solitary wave solutions are rational, trigonometric, hyperbolic, elliptic functions including dark, bright, singular, combined, optical solitons, kink wave, anti-kink wave, periodic wave, travelling wave and we also represent the physical interpretation of new solutions by 2D and 3D graphical by using the Mathematica. These constructed solutions may play vital role in the areas of Mathematical physics, plasma physics, nonlinear optics, quantum mechanics, fluid dynamics and many different fields of applied sciences. The complete calculations show that this new technique is more powerful, effective, straightforward and we can also apply on other nonlinear PDEs involves in Mathematical physics and many other physical sciences.
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nonlinear wave solutions of the kudryashov sinelshchikov Dynamical Equation in mixtures liquid gas bubbles under the consideration of heat transfer and viscosity
Journal of Taibah University for Science, 2019Co-Authors: Aly R Seadawy, Mujahid IqbalAbstract:In this research, we constructed the exact travelling and solitary wave solutions of the Kudryashov–Sinelshchikov (KS) Equation by implementing the modified mathematical method. The KS Equation des...
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modulation stability analysis and solitary wave solutions of nonlinear higher order schrodinger Dynamical Equation with second order spatiotemporal dispersion
Indian Journal of Physics, 2019Co-Authors: Aly R Seadawy, Muhammad ArshadAbstract:In optical fibers, the higher-order nonlinear Schrodinger (NLS) Dynamical Equation which describes the beyond the classic slowly varying envelopes and spatiotemporal dispersion of pulses is investigated. By applying the proposed modified extended mapping method, the optical soliton solutions of higher-order NLS Dynamical Equation with the coefficients of group velocity dispersion, second-order spatiotemporal dispersion and cubic nonlinearity are deduced. The obtained solutions have important applications in applied sciences and engineering. The formation conditions are specified on parameters in which optical solitons can exist for this media. The moments of some constructed solutions are presented graphically which facilitate the researchers to comprehend the physical phenomena of this Equation. The modulation instability analysis is utilized to discuss the model stability, which verifies that all obtained solutions are stable and exact. Other such forms of the system arising in sciences and engineering can also be solved by this steadfast, influential and effective method.
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mixed lump solitons periodic lump and breather soliton solutions for 2 1 dimensional extended kadomtsev petviashvili Dynamical Equation
International Journal of Modern Physics B, 2019Co-Authors: Iftikhar Ahmed, Aly R SeadawyAbstract:In this study, based on the Hirota bilinear method, mixed lump-solitons, periodic lump and breather soliton solutions are derived for (2 + 1)-dimensional extended KP Equation with the aid of symbol...
Michel Jean - One of the best experts on this subject based on the ideXlab platform.
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Non-smooth contact dynamics approach of cohesive materials
Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences (1934-1990), 2001Co-Authors: Michel Jean, Vincent Acary, Yann MonerieAbstract:The main features of the non-smooth contact dynamics (NSCD) method—the Dynamical Equation, the Signorini relation as a non-smooth modelling of unilateral contact, and the frictional Coulomb's law, treated with fully implicit algorithms— are briefly presented in this paper. By mere changes of variables, it appears that a large class of interface problems, including cohesive interface problems, may be solved using Signorini, Coulomb and standard NSCD algorithms. Emphasis is put on contact between deformable bodies. Examples illustrating numerical simulation are given for fibre-reinforced materials and for buildings made of blocks.
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The non-smooth contact dynamics method
Computer Methods in Applied Mechanics and Engineering, 1999Co-Authors: Michel JeanAbstract:The main features of the Non-Smooth Contact Dynamics method are presented in this paper, the use of the Dynamical Equation, the non-smooth modelling of unilateral contact and Coulomb's law, fully implicit algorithms to solve the Dynamical frictional contact problem for systems with numerous contacting points, in particular large collections of rigid or deformable bodies. Emphasis is put on contact between deformable bodies. Illustrating numerical simulation examples are given for granular materials, deep drawing and buildings made of stone blocks.
Mujahid Iqbal - One of the best experts on this subject based on the ideXlab platform.
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construction of soliton solutions of the modify unstable nonlinear schrodinger Dynamical Equation in fiber optics
Indian Journal of Physics, 2020Co-Authors: Aly R Seadawy, Mujahid IqbalAbstract:In this research article, we investigated the universal model of integrable system of modify unstable nonlinear Schrodinger Equation. The mUNLSE described the disturbance of time period in slightly stable and unstable media and managed the instability of modulation wave train. We found the exact and solitary wave solutions of mUNLSE with the help of modified extended auxiliary Equation mapping method. As a result, exact and solitary wave solutions in the form of elliptic functions, trigonometric functions, hyperbolic functions, bright and dark solitons, traveling wave, kink-type solitons and periodic solitary wave solution are obtained. These solutions show the power and effectiveness of this new method and two- and three-dimensional graphically with the help of computer software Mathematica. We can also solve other unstable nonlinear system of PDEs which are involved in Mathematical physics and many other branches of physical sciences with the help of this new method.
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propagation of long internal waves in density stratified ocean for the 2 1 dimensional nonlinear nizhnik novikov vesselov Dynamical Equation
Results in physics, 2020Co-Authors: Mujahid Iqbal, Aly R Seadawy, O H KhalilAbstract:Abstract Our aim in this article to constructed the new solitary wave solutions of (2+1)-dim nonlinear Nizhnik-Novikov-Vesselov Equation by novel approach which is extended modified rational expansion method. The new solitary wave solutions are rational, trigonometric, hyperbolic, elliptic functions including dark, bright, singular, combined, optical solitons, kink wave, anti-kink wave, periodic wave, travelling wave and we also represent the physical interpretation of new solutions by 2D and 3D graphical by using the Mathematica. These constructed solutions may play vital role in the areas of Mathematical physics, plasma physics, nonlinear optics, quantum mechanics, fluid dynamics and many different fields of applied sciences. The complete calculations show that this new technique is more powerful, effective, straightforward and we can also apply on other nonlinear PDEs involves in Mathematical physics and many other physical sciences.
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nonlinear wave solutions of the kudryashov sinelshchikov Dynamical Equation in mixtures liquid gas bubbles under the consideration of heat transfer and viscosity
Journal of Taibah University for Science, 2019Co-Authors: Aly R Seadawy, Mujahid IqbalAbstract:In this research, we constructed the exact travelling and solitary wave solutions of the Kudryashov–Sinelshchikov (KS) Equation by implementing the modified mathematical method. The KS Equation des...
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dispersive solitary wave solutions of nonlinear further modified korteweg de vries Dynamical Equation in an unmagnetized dusty plasma
Modern Physics Letters A, 2018Co-Authors: Mujahid Iqbal, Aly R SeadawyAbstract:In this work, we consider the propagation of one-dimensional nonlinear unmagnetized dusty plasma, by using the reductive perturbation technique to formulate the nonlinear mathematical model which is further modified Korteweg–de Vries (fmKdV) Dynamical Equation. We use the extend form of two methods, auxiliary Equation mapping and direct algebraic methods, to investigate the families of dust and ion solitary wave solutions of one-dimensional nonlinear fmKdV. These new exact and solitary wave solutions, which represent the electrostatic potential and pressure for fmKdV, and also the graphical representation of electrostatic potential and pressure are shown with the aid of Mathematica.
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construction of solitary wave solutions to the nonlinear modified kortewege de vries Dynamical Equation in unmagnetized plasma via mathematical methods
Modern Physics Letters A, 2018Co-Authors: Mujahid Iqbal, Aly R SeadawyAbstract:In this research, we consider the propagation of one-dimensional nonlinear behavior in a unmagnetized plasma. By using the reductive perturbation technique to formulate the nonlinear mathematic mod...
Itamar Procaccia - One of the best experts on this subject based on the ideXlab platform.
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exact solution for the energy spectrum of kelvin wave turbulence in superfluids
Physical Review B, 2011Co-Authors: Laurent Boue, Ratul Dasgupta, Jason Laurie, Victor S Lvov, S Nazarenko, Itamar ProcacciaAbstract:We study the statistical and Dynamical behavior of turbulent Kelvin waves propagating on quantized vortices in superfluids and address the controversy concerning the energy spectrum that is associated with these excitations. Finding the correct energy spectrum is important because Kelvin waves play a major role in the dissipation of energy in superfluid turbulence at near-zero temperatures. In this paper, we show analytically that the solution proposed by [L’vov and Nazarenko, JETP Lett. 91, 428 (2010)] enjoys existence, uniqueness, and regularity of the prefactor. Furthermore, we present numerical results of the Dynamical Equation that describes to leading order the nonlocal regime of the Kelvin-wave dynamics. We compare our findings with the analytical results from the proposed local and nonlocal theories for Kelvin-wave dynamics and show an agreement with the nonlocal predictions. Accordingly, the spectrum proposed by L’vov and Nazarenko should be used in future theories of quantum turbulence. Finally, for weaker wave forcing we observe an intermittent behavior of the wave spectrum with a fluctuating dissipative scale, which we interpreted as a finite-size effect characteristic of mesoscopic wave turbulence.
Jun Wang - One of the best experts on this subject based on the ideXlab platform.
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three dimensional nonlinear extended zakharov kuznetsov Dynamical Equation in a magnetized dusty plasma via acoustic solitary wave solutions
Brazilian Journal of Physics, 2019Co-Authors: Aly R Seadawy, Jun WangAbstract:The propagation of nonlinear three-dimensional dust-ion-acoustic solitary waves in a magnetized two-ion-temperature dusty plasma is analyzed. Modified extended mapping method is further modified to discover dust-ion-acoustic solitary wave solutions of the nonlinear three-dimensional extended Zakharov-Kuznetsov Dynamical Equation. Consequently, different kinds of solitary wave solutions representing electric potential, electric and magnetic fields, and electron fluid pressure, are obtained with the help of Mathematica. The new dispersive solitary wave solutions are found in various shapes such as bright and dark solitons, periodic solitary wave solutions, and dark and bright solitary waves, that are expressed in different forms such as hyperbolic, rational, exponential, and trigonometric functions. These results demonstrate the efficiency and accuracy of the proposed method that can be applied to other nonlinear models. The results are shown graphically.
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modified kdv zakharov kuznetsov Dynamical Equation in a homogeneous magnetised electron positron ion plasma and its dispersive solitary wave solutions
Pramana, 2018Co-Authors: Aly R Seadawy, Jun WangAbstract:Propagation of three-dimensional nonlinear ion-acoustic solitary waves and shocks in a homogeneous magnetised electron–positron–ion plasma is analysed. Modified extended mapping method is introduced to find ion-acoustic solitary wave solutions of the three-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov Equation. As a result, solitary wave solutions (which represent electrostatic field potential), electric fields, magnetic fields and quantum statistical pressures are obtained with the aid of Mathematica. These new exact solitary wave solutions are obtained in different forms such as periodic, kink and antikink, dark soliton, bright soliton, bright and dark solitary wave etc. The results are expressed in the forms of hyperbolic, trigonometric, exponential and rational functions. The electrostatic field potential and electric and magnetic fields are shown graphically. These results demonstrate the efficiency and precision of the method that can be applied to many other mathematical and physical problems.
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Recurrent Neural Networks for Computing Pseudoinverses of Rank-Deficient Matrices
SIAM Journal on Scientific Computing, 1997Co-Authors: Jun WangAbstract:Three recurrent neural networks are presented for computing the pseudoinverses of rank-deficient matrices. The first recurrent neural network has the Dynamical Equation similar to the one proposed earlier for matrix inversion and is capable of Moore--Penrose inversion under the condition of zero initial states. The second recurrent neural network consists of an array of neurons corresponding to a pseudoinverse matrix with decaying self-connections and constant connections in each row or column. The third recurrent neural network consists of two layers of neuron arrays corresponding, respectively, to a pseudoinverse matrix and a Lagrangian matrix with constant connections. All three recurrent neural networks are also composed of a number of independent subnetworks corresponding to the rows or columns of a pseudoinverse. The proposed recurrent neural networks are shown to be capable of computing the pseudoinverses of rank-deficient matrices.
