Novel nonlinear wave equation: Regulated rogue waves and accelerated soliton solutions

Abstract

A new exactly solvable (1+1)-dimensional complex nonlinear wave equation exhibiting rich analytic properties has been introduced. A rogue wave (RW), localized in space-time like Peregrine RW solution, though richer due to the presence of free parameters is discovered. This freedom allows to regulate amplitude and width of the RW as needed. The proposed equation allows also an intriguing topology changing accelerated dark soliton solution in spite of constant coefficients in the equation.

Diverse high-order soliton solutions and novel hybrid behaviors for the (2+1)-dimensional KP-BBM equation

“…In recent decades, several methods and frameworks for NLEEs have been developed, including the Hirota bilinear transformation [1,2], Grammian determinant technique based on Sato operator theory [3,4], the long wave limit method [5,6], and the Darboux transformation [7], and so on [8,9]. NLEEs contains those new parsing structures, examples like breathers, hybrid solutions, soliton molecules, lump solutions and rogue waves have been researched [10,11,12,13,14,15,16,17,18,19]. Especially, it is evident that the long wave limit method is a very advantageous technique for solving the rational solutions of nonlinear evolution equations, which is more concise compared to typical methods to obtain some new analytical solutions, thereby finding accurate solutions to NLEEs.…”

Bending of solitonic beams modelled by coupled KMN equation in optical birefringent fibers

“…On the other hand, the presence of lossy or time dependent terms in the evolution equation makes it non-integrable causing the velocity of solitary waves to change. Recently, a deep research interest has been developed on some special intricate exact solutions of nonlinear systems like accelerating solitons [7][8][9], topological solitons [10][11][12][13][14], rogue wave solutions [15,16] etc.…”

Novel curved lump and topological solitons of integrable (2+1) dimensional KMN equation

“…Line soliton solutions which are exact stable localized solutions of completely integrable systems, have been explored extensively in the past few decades [1,2]. However, in recent years, a deep research interest has been developed on some special intricate solutions like accelerating solitons [3][4][5], topologically nontrivial solutions [6][7][8], rogue wave solutions [9,10] etc. Recently a new completely integrable (2+1) dimensional nonlinear evolution equation has been derived by Anjan Kundu, Abhik Mukherjee and Tapan Naskar to describe the dynamics of two-dimensional oceanic rogue wave phenomena [9].…”