Some new nonlinear wave solutions and dynamical behavior of the (3+1)-dimensional Ito equation

Abstract

Some new nonlinear wave solutions of the (3+1)-dimensional Ito equation, such as three-wave type solutions, lump wave solutions, rogue wave solutions and hybrid solutions of different forms, are studied by the bilinear neural network method. Besides, three-wave solutions are investigated via the single-layer neural network ‘4-3-1’ model, and hybrid soliton solutions between lump-type and strip-like soliton in ‘4-5-1’ model are discussed. Furthermore, rogue wave solutions are studied by the double-layer neural network the ‘4-2-3-1’ and the ‘4-3-3-1’ models, and the interference phenomena between them are analyzed using visual images. We also employed the extended parameter limit method to investigate the collapse degradation behavior of both solutions. Lump solutions and Y-type semi-rational solutions are derived separately.

Keywords

• (3+1)-dimensional Ito equation
• Bilinear neural network method
• Dynamic behavior
• Rogue wave
• Three-wave type
• Lump solution