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The singular manifold method and exact periodic wave solutions to a restricted BLP dispersive long wave system. (English) Zbl 1090.35159

Summary: The singular manifold method, with a new algorithm, is applied to a restricted Boiti-Leon-Pempinelli (BLP) dispersive long wave system. A general solution involving three arbitrary functions is then obtained for the equation in question. Exact periodic wave solutions are thus expressed as rational functions of the Jacobi elliptic functions by choosing appropriately these arbitrary functions. Interaction of Jacobi elliptic waves is studied numerically and found to be nonelastic! Long wave limits yield some new types of solitary waves, dromion-like and solitoff-like structures. New types of solitary waves manifest new features of interactions, i.e., after the interaction of two groups of solitary waves, one is elastic and the other is nonelastic, which has not been reported previously.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
35L70 Second-order nonlinear hyperbolic equations
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