One-dimensional space

Quantum mechanics

Algorithm

Rogue wave

Mathematical physics

Statistics

Symbolic computation

Lax pair

Applied mathematics

Nonlinear Schrödinger equation

Computation

Soliton

Bilinear form

Thermodynamics

Physics

Nonlinear system

Integrable system

Mathematics

Bilinear interpolation

Waves and shallow water

Mathematical analysis

Traveling wave

Schrödinger equation

Applied Mathematics Letters

Waves are seen in the atmosphere, oceans, etc. As one of the most common natural phenomena, water waves attract the attention of researchers. For the shallow water waves, a (3+1)-dimensional generalized nonlinear evolution equation is hereby investigated via the symbolic computation. Based on the Hirota method, we present three bilinear auto-Bäcklund transformations, along with some soliton solutions. Our results depend on the water-wave coefficients in that equation.

Bilinear auto-Bäcklund transformations and soliton solutions of a (3+1)-dimensional generalized nonlinear evolution equation for the shallow water waves