Bäcklund Transformation, Lax Pair and Solitons of the (2+1)-dimensional Davey-Stewartson-like Equations with Variable Coefficients for the Electrostatic Wave Packets

Abstract

The (2+1)-dimensional Davey-Stewartson-like equations with variable coefficients have the applications in the ultra-relativistic degenerate dense plasmas and Bose-Einstein condensates. Via the Bell polynomials and symbolic computation, the bilinear form, Bäcklund transformation and Lax pair for such equations are obtained. Based on the Hirota method, we construct the soliton solutions, analyze the elastic collisions with the constant and variable coefficients, and observe that solitons no longer keep rectilinear propagation and display different shapes because of the variable coefficients. Besides, localized excitations are derived through the variable separation.

Novel solitons and periodic wave solutions for Davey–Stewartson system with variable coefficients

“…Many novel wave solutions have been obtained in the previous section are considered new for the vcDS compared to other solutions obtained previously in the literature [22,41,42]. In this section, a discussion for the plots of the complex wave envelope | 1 |, by assuming that m 2 = 0 in (8), are presented.…”

“…Therefore, we conclude that the similarity methodology used in this paper is more efficient and easier to apply compared to the classical Lie group method. Moreover, many exact solutions are obtained for the vcDS considered new compared to other solutions obtained before in [22,41,42].…”

“…where = (t, x, y), and = (t, x, y) are the complex wave envelope and the real forcing terms, respectively. Note that a 1 , a 2 , b 1 and b 2 are real functions in t, where a 1 and a 2 are corresponding to the group velocity dispersion (GVD) terms and b 1 and b 2 represent the nonlinear cubic coefficient and quadratic nonlinearity terms while s 1 and s 2 are real constants (for more details about the physical background of the vcDS system see [41,42]). Recently, Zhou et al [41] solve the vcDs for Lax pair and Bäcklund transformation.…”

“…Note that a 1 , a 2 , b 1 and b 2 are real functions in t, where a 1 and a 2 are corresponding to the group velocity dispersion (GVD) terms and b 1 and b 2 represent the nonlinear cubic coefficient and quadratic nonlinearity terms while s 1 and s 2 are real constants (for more details about the physical background of the vcDS system see [41,42]). Recently, Zhou et al [41] solve the vcDs for Lax pair and Bäcklund transformation. Moreover, Wei et al [42] obtain conservation laws and similarity solutions using the classical Lie group.…”

Oceanic Shallow-Water Investigations on a Variable-Coefficient Davey–Stewartson System

“…The Davey-Stewartson (DS) equations are an important and nontrivial integrable model originally used to describe a (2 + 1)-dimensional wave packet on the surface of a liquid of finite depth [21][22][23]. The DS equation is divided into two types, the DS-I and DS-II equations, depending on the strength of surface tension [24,25]. The DS-I equation is written as follows:…”