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Multiple soliton-like solutions for \((2+1)\)-dimensional dispersive long-wave equations. (English) Zbl 0940.35180

Summary: By using a homogeneous balance method, multiple-soliton-like solutions of the \((2+1)\)-dimensional dispersive long-wave equation \[ \begin{aligned} u_{ty}+ \eta_{xx}+ u_x u_y+ uu_{xy} & = 0,\\ \eta_t+ (u\eta+ u+ y_{xy})_x & = 0\end{aligned} \] are constructed. The method used here can be generalized to a wide class of nonlinear evolution equations.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35C05 Solutions to PDEs in closed form
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