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Interaction between line soliton and \(y\)-periodic soliton: solutions to the asymmetric Nizhnik-Novikov-Veselov equation. (English) Zbl 1086.35096

Summary: A variable separation approach is used to obtain exact solutions of the asymmetric Nizhnik-Novikov-Veselov equation \[ u_t+ u_{xxx}+3[uv]_x=0,\quad u_x=v_y. \] Some exact solutions of this model are analyzed to study the interaction between line soliton and \(y\)-periodic soliton. The interactions are classified into several types according to the phase shifts due to collisions.

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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