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Bäcklund transformation, Lax pair and solitons of the \((2+1)\)-dimensional Davey-Stewartson-like equations with variable coefficients for the electrostatic wave packets. (English) Zbl 1420.35336
Summary: 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.
MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35Q55 NLS equations (nonlinear Schrödinger equations)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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