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Homogeneous balance method and chaotic and fractal solutions for the Nizhnik-Novikov-Veselov equation. (English) Zbl 1040.35105

Summary: The Bäcklund transformation (BT) for the Nizhnik-Novikov-Veselov (NNV) equation is derived by using the extended homogeneous balance method. By means of the BT, a rather general variable separation solution of the model is obtained. The chaotic and fractal solution structures of the model are constructed by the entrance of two variable-separated arbitrary functions.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems
35C05 Solutions to PDEs in closed form
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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