Lump and new interaction solutions to the (3+1)-dimensional nonlinear evolution equation

Abstract

In this paper, a new (3+1)-dimensional nonlinear evolution equation is introduced, through the generalized bilinear operators based on prime number p = 3. By Maple symbolic calculation, one-, two-lump, and breather-type periodic soliton solutions are obtained, where the condition of positiveness and analyticity of the lump solution are considered. The interaction solutions between the lump and multi-kink soliton, and the interaction between the lump and breather-type periodic soliton are derived, by combining multi-exponential function or trigonometric sine and cosine functions with a quadratic one. In addition, new interaction solutions between a lump, periodic-solitary waves, and one-, two- or even three-kink solitons are constructed by using the ansatz technique. Finally, the characteristics of these various solutions are exhibited and illustrated graphically.

Nondegenerate solitons for coupled higher-order nonlinear Schrödinger equations in optical fibers

“…The asterisk denotes the complex conjugate. In principle, multi-soliton are constructed by the series expansions of g, h and f. Unlike the normal bilinear construction [19][20][21], we set the nondegenerate one-soliton solutions for CHNLSE (1) by special forms as…”

Superposition formulas of multi-solution to a reduced (3+1)-dimensional nonlinear evolution equation

“…Besides, Shi et al [39] used this method and KP hierarchy reduction method to get the general high-order rogue waves. Asma Issasfa et al [40] obtained the generalized bilinear form through the generalized Hirota bilinear method to get new lump solutions and interaction solutions. Lou converted the bilinear forms of some NLEEs into the full reversal symmetric forms and obtained multiple soliton solutions.…”