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Infinite sequences solutions of \((2 + 1)\)-dimensional asymmetric Nizhnik-Novikov-Veselov system. (Chinese. English summary) Zbl 1424.35303

Summary: A method combining function transformation and the second elliptic equation is given. With the aid of known solutions of the second elliptic equation and related results of solutions, the new solutions of \((2 + 1)\)-dimensional asymmetric Nizhnik-Novikov-Veselov system are presented, which include infinite sequences composed by hyperbolic function and the arbitrary one of the Jacobi elliptic function, Riemann \(\theta\) function and trigonometric functions, and two-soliton solutions and double-periodic solutions. Some features of the obtained solutions are analyzed by using numerical simulation approach with the aid of symbolic computation system Mathematica.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B10 Periodic solutions to PDEs
35C08 Soliton solutions

Software:

Mathematica
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