Topological Solitons of the Nonlinear Schrödinger’s Equation with Fourth Order Dispersion

Abstract

This paper obtains the topological 1-soliton solution of the nonlinear Schrödin-ger's equation, in a non-Kerr law media, with fourth order dispersion. An exact 1-soliton solution is obtained. The types of nonlinearity that are studied in this paper are Kerr law and power law.

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

“…where we have chosen β 1 = β 1 = β for mathematical convenience which does not violate the generality of the problem. Hence, by choosing γ 1 = γ 2 = 0, we get a constant coefficient ode ( 11) from (7) in spite of the presence of arbitrary functions A(X), B(X) in the solution (5). This is a rare feature which is present in the KMN equation ( 2) due to it's current like nonlinearity (nonlinear term is a function of U and U X ).…”

“…There has been a continued interest in the field of fascinating topological soliton solutions [6][7][8] both in physics and mathematics. Exact one topological line soliton solution with constant amplitude and velocity of the KMN equation ( 1) is derived in [30].…”

“…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].…”

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

“…and "R" and "I" in the subscripts denote the real and imaginary parts of the complex constants. In the above simplification, we have chosen the arbitrary constants η 0R , η 0I , φ, θ, δ 1 in such a way that they get cancelled and we get the expressions (11). The 3 -dimensional plots of the two bright solitonic modes u and v are shown in FIG.…”

“…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.…”