The Experts below are selected from a list of 2334 Experts worldwide ranked by ideXlab platform
Zhenya Yan - One of the best experts on this subject based on the ideXlab platform.
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abundant families of jacobi elliptic function solutions of the 2 1 dimensional integrable davey Stewartson type equation via a new method
Chaos Solitons & Fractals, 2003Co-Authors: Zhenya YanAbstract:Our extended Jacobi elliptic function expansion method is further improved to be a more powerful method, which is still called the extended Jacobi elliptic function expansion method, by using 12 Jacobi elliptic functions. The new (2+1)-dimensional integrable Davey–Stewartson-type is chosen to illustrate the approach. As a consequence, 24 families of Jacobi elliptic function solutions are obtained. When the modulus m→1, these doubly periodic solutions degenerate as soliton solutions. The method can be also applied to other nonlinear differential equations.
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symbolic computation and weierstrass elliptic function solutions of the davey Stewartson ds system
International Journal of Modern Physics C, 2003Co-Authors: Zhenya YanAbstract:In this paper, with the symbolic computation, the doubly-periodic solutions of the Davey–Stewartson (DS) system, which describes the modulational instability of uniform train of weakly nonlinear water waves in the two-dimensional space, are investigated in terms of the Weierstrass elliptic function ℘(ξ; g2, g3). In particular, we also give new solitary wave solutions of this system.
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jacobi elliptic function solutions of nonlinear wave equations via the new sinh gordon equation expansion method
Journal of Physics A, 2003Co-Authors: Zhenya YanAbstract:In this paper, based on the well-known sinh-Gordon equation, a new sinh-Gordon equation expansion method is developed. This method transforms the problem of solving nonlinear partial differential equations into the problem of solving the corresponding systems of algebraic equations. With the aid of symbolic computation, the procedure can be carried out by computer. Many nonlinear wave equations in mathematical physics are chosen to illustrate the method such as the KdV-mKdV equation, (2+1)-dimensional coupled Davey–Stewartson equation, the new integrable Davey–Stewartson-type equation, the modified Boussinesq equation, (2+1)-dimensional mKP equation and (2+1)-dimensional generalized KdV equation. As a consequence, many new doubly-periodic (Jacobian elliptic function) solutions are obtained. When the modulus m → 1 or 0, the corresponding solitary wave solutions and singly-periodic solutions are also found. This approach can also be applied to solve other nonlinear differential equations.
Tsuchida Takayuki - One of the best experts on this subject based on the ideXlab platform.
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Integrable semi-discretizations of the Davey-Stewartson system and a $(2+1)$-dimensional Yajima-Oikawa system. II
2020Co-Authors: Tsuchida TakayukiAbstract:This is a continuation of our previous paper arXiv:1904.07924, which is devoted to the construction of integrable semi-discretizations of the Davey-Stewartson system and a $(2+1)$-dimensional Yajima-Oikawa system; in this series of papers, we refer to a discretization of one of the two spatial variables as a semi-discretization. In this paper, we construct an integrable semi-discrete Davey-Stewartson system, which is essentially different from the semi-discrete Davey-Stewartson system proposed in the previous paper arXiv:1904.07924. We first obtain integrable semi-discretizations of the two elementary flows that compose the Davey-Stewartson system by constructing their Lax-pair representations and show that these two elementary flows commute as in the continuous case. Then, we consider a linear combination of the two elementary flows to obtain a new integrable semi-discretization of the Davey-Stewartson system. Using a linear transformation of the continuous independent variables, one of the two elementary Davey-Stewartson flows can be identified with an integrable semi-discretization of the $(2+1)$-dimensional Yajima-Oikawa system proposed in https://link.aps.org/doi/10.1103/PhysRevE.91.062902 .Comment: 16 page
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Integrable semi-discretizations of the Davey-Stewartson system and a $(2+1)$-dimensional Yajima-Oikawa system. I
2020Co-Authors: Tsuchida TakayukiAbstract:The integrable Davey-Stewartson system is a linear combination of the two elementary flows that commute: $\mathrm{i} q_{t_1} + q_{xx} + 2q\partial_y^{-1}\partial_x (|q|^2) =0$ and $\mathrm{i} q_{t_2} + q_{yy} + 2q\partial_x^{-1}\partial_y (|q|^2) =0$. In the literature, each elementary Davey-Stewartson flow is often called the Fokas system because it was studied by Fokas in the early 1990s. In fact, the integrability of the Davey-Stewartson system dates back to the work of Ablowitz and Haberman in 1975; the elementary Davey-Stewartson flows, as well as another integrable $(2+1)$-dimensional nonlinear Schr\"odinger equation $\mathrm{i} q_{t} + q_{xy} + 2 q\partial_y^{-1}\partial_x (|q|^2) =0$ proposed by Calogero and Degasperis in 1976, appeared explicitly in Zakharov's article published in 1980. By applying a linear change of the independent variables, an elementary Davey-Stewartson flow can be identified with a $(2+1)$-dimensional generalization of the integrable long wave-short wave interaction model, called the Yajima-Oikawa system: $\mathrm{i} q_{t} + q_{xx} + u q=0$, $u_t + c u_y = 2(|q|^2)_x$. In this paper, we propose a new integrable semi-discretization (discretization of one of the two spatial variables, say $x$) of the Davey-Stewartson system by constructing its Lax-pair representation; the two elementary flows in the semi-discrete case indeed commute. By applying a linear change of the continuous independent variables to an elementary flow, we also obtain an integrable semi-discretization of the $(2+1)$-dimensional Yajima-Oikawa system.Comment: 17 pages; (v2) improved introduction and added one referenc
Saadet Erbay - One of the best experts on this subject based on the ideXlab platform.
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standing waves for a generalized davey Stewartson system
Journal of Physics A, 2006Co-Authors: A Eden, Saadet ErbayAbstract:In this paper, we establish the existence of non-trivial solutions for a semi-linear elliptic partial differential equation with a non-local term. This result allows us to prove the existence of standing wave (ground state) solutions for a generalized Davey–Stewartson system. A sharp upper bound is also obtained on the size of the initial values for which solutions exist globally.
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two dimensional wave packets in an elastic solid with couple stresses
International Journal of Non-linear Mechanics, 2004Co-Authors: Ceni Babaoglu, Saadet ErbayAbstract:Abstract The problem of (2+1) (two spatial and one temporal) dimensional wave propagation in a bulk medium composed of an elastic material with couple stresses is considered. The aim is to derive (2+1) non-linear model equations for the description of elastic waves in the far field. Using a multi-scale expansion of quasi-monochromatic wave solutions, it is shown that the modulation of waves is governed by a system of three non-linear evolution equations. These equations involve amplitudes of a short transverse wave, a long transverse wave and a long longitudinal wave, and will be called the “generalized Davey–Stewartson equations”. Under some restrictions on parameter values, the generalized Davey–Stewartson equations reduce to the Davey–Stewartson and to the non-linear Schrodinger equations. Finally, some special solutions involving sech–tanh–tanh and tanh–tanh–tanh type solitary wave solutions are presented.
Anjan Biswas - One of the best experts on this subject based on the ideXlab platform.
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cnoidal and snoidal wave solutions to coupled nonlinear wave equations by the extended jacobi s elliptic function method
Communications in Nonlinear Science and Numerical Simulation, 2013Co-Authors: M A Abdelkawy, A H Bhrawy, Anjan BiswasAbstract:Abstract This paper studies two nonlinear coupled evolution equations. They are the Zakharov equation and the Davey–Stewartson equation. These equations are studied by the aid of Jacobi’s elliptic function expansion method and exact periodic solutions are extracted. In addition, the Zakharov equation with power law nonlinearity is solved by traveling wave hypothesis.
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analytical and numerical solutions to the davey Stewartson equation with power law nonlinearity
Waves in Random and Complex Media, 2011Co-Authors: Ghodrat Ebadi, E V Krishnan, Manel Labidi, Essaid Zerrad, Anjan BiswasAbstract:This paper studies the Davey–Stewartson equation. The traveling wave solution of this equation is obtained for the case of power-law nonlinearity. Subsequently, this equation is solved by the exponential function method. The mapping method is then used to retrieve more solutions to the equation. Finally, the equation is studied with the aid of the variational iteration method. The numerical simulations are also given to complete the analysis.
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the g g method and 1 soliton solution of the davey Stewartson equation
Mathematical and Computer Modelling, 2011Co-Authors: Ghodrat Ebadi, Anjan BiswasAbstract:This paper studies the Davey-Stewartson equation. The G^'G method is applied to carry out the integration of this equation. Subsequently, using the ansatz method this equation is integrated in (1+2) dimensions with power law nonlinearity.
A S Fokas - One of the best experts on this subject based on the ideXlab platform.
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davey Stewartson type equations in 4 2 and 3 1 possessing soliton solutions
Journal of Mathematical Physics, 2013Co-Authors: M Dimakos, A S FokasAbstract:An integrable generalisation of a Davey-Stewartson type system of two equations involving two scalar functions in 4+2, i.e., in four spatial and two temporal dimensions, has been recently derived by one of the authors. Here, we first show that there exists a reduction of this system to a single equation involving a scalar function in 4+2; we will refer to this equation as the 4+2 Davey-Stewartson equation. We then show that it is possible to reduce this equation to an equation in 3+1, which we will refer to as the 3+1 Davey-Stewartson equation. Furthermore, by employing the so-called direct linearising method, we compute 1- and 2-soliton solutions for both the 4+2 and the 3+1 Davey-Stewartson equations.
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the davey Stewartson equation on the half plane
Communications in Mathematical Physics, 2009Co-Authors: A S FokasAbstract:The Davey-Stewartson (DS) equation is a nonlinear integrable evolution equation in two spatial dimensions. It provides a multidimensional generalisation of the celebrated nonlinear Schrodinger (NLS) equation and it appears in several physical situations. The implementation of the Inverse Scattering Transform (IST) to the solution of the initial-value problem of the NLS was presented in 1972, whereas the analogous problem for the DS equation was solved in 1983. These results are based on the formulation and solution of certain classical problems in complex analysis, namely of a Riemann Hilbert problem (RH) and of either a d-bar or a non-local RH problem respectively. A method for solving the mathematically more complicated but physically more relevant case of boundary-value problems for evolution equations in one spatial dimension, like the NLS, was finally presented in 1997, after interjecting several novel ideas to the panoply of the IST methodology. Here, this method is further extended so that it can be applied to evolution equations in two spatial dimensions, like the DS equation. This novel extension involves several new steps, including the formulation of a d-bar problem for a sectionally non-analytic function, i.e. for a function which has different non-analytic representations in different domains of the complex plane. This, in addition to the computation of a d-bar derivative, also requires the computation of the relevant jumps across the different domains. This latter step has certain similarities (but is more complicated) with the corresponding step for those initial-value problems in two dimensions which can be solved via a non-local RH problem, like KPI.
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on the solvability of the n wave davey Stewartson and kadomtsev petviashvili equations
Inverse Problems, 1992Co-Authors: A S Fokas, Liyeng SungAbstract:The authors review a rigorous methodology for studying the initial-value problem, for decaying initial data on the plane, for integrable evolution equations in two spatial variables. The N-wave interaction, the Davey-Stewartson and the Kadomtsev-Petviashvili equations are used as illustrative examples. They discuss both the use of a nonlocal Riemann-Hilbert problem and of a delta (DBAR) problem. Some of the results reviewed here are valid only if the initial data satisfy a certain small-norm condition, while some are valid without any small-norm condition.
