Bilinearization of a Generalized Derivative Nonlinear Schrödinger Equation

Abstract

A generalized derivative nonlinear Schrödinger equation,is studied by means of Hirota's bilinear formalism. Soliton solutions are constructed as quotients of Wronski-type determinants. A relationship between the bilinear structure and gauge transformation is also discussed. *

Integrable Hierarchy of Higher Nonlinear Schrödinger Type Equations

“…Note that though both equations (2.1), (2.2) have been studied quite extensively [13,14,15], the investigations were confined mostly to the particular functional choice for θ as θ = δ x |Q(x )| 2 dx , with a real parameter δ. Under this choice the NLSE (1.1) is extended to the Eckhaus-Kundu (EK) equation [11,12,16,17,18] …”

Solutions of a Derivative Nonlinear Schrödinger Hierarchy and Its Similarity Reduction

“…The solutions obtained are expressed in terms of "double Wronskians" (3.12). We remark that the double Wronskian solutions for the ∂NLS equation have been obtained in [11] by using Hirota's bilinear formulation. …”

Soliton Solutions of the N = 2 Supersymmetric KP Equation

“…Of these the Hirota method [10] has also been used extensively to find soliton solutions of a number of supersymmetric integrable equations. In bosonic integrable systems, this formalism has been widely applied to obtain the soliton solutions of a large number of nonlinear evolution equations (see for example [11][12][13][14][15][16][17][18][19][20]). However, in its supersymmetric extension the Hirota method has been applied mainly to N = 1 supersymmetric integrable systems [21][22][23][24][25].…”