All first- and second-order (2+1)-dimensional nonlinear wave equations derived from the Euler equations for an ideal fluid model and their traveling wave solutions
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引用次数: 0
Abstract
We review the (2+1)-dimensional nonlinear wave equations we recently derived from the ideal fluid model. These are extensions of the KdV, fifth-order KdV, Gardner, extended KdV and extended KP equations into two spatial dimensions. We discuss analytical solutions to these equations in the form of traveling waves. All these solutions, soliton, cnoidal, and superposition ones, are analogous to solutions of the corresponding (1+1)-dimensional equations. The complete (2+1)-dimensional fifth-order KdV equation, (2+1)-dimensional Gardner equation, and their soliton solutions are derived here for the first time.
期刊介绍：
Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics.
The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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