Related papers: Darboux Transformation for the Hirota equation
Solitons in nonlinear optics holds a special role both in theoretical and experimental studies. Several types of evolution equations are seen to govern different situation of physical relevance. One such is the existence of both resonant…
In this paper, We extend the two-component coupled Hirota equation to the three-component one, and reconstruct the Lax pair with $4\times4$ matrixes of this three-component coupled system including higher-order effects such as third-order…
A new form of a binary Darboux transformation is used to generate analytical solutions of a nonlinear Liouville-von Neumann equation. General theory is illustrated by explicit examples.
Based on our previous work to the Degasperis-Procesi equation (J. Phys. A 46 045205) and the integrable semi-discrete analogue of its short wave limit (J. Phys. A 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation…
Hirota's bilinear method ("direct method") has been very effective in constructing soliton solutions to many integrable equations. The construction of one- and two-soliton solutions is possible even for non-integrable bilinear equations,…
We show that we can also apply the Hirota method to some non-integrable equations. For this purpose, we consider the extensions of the Kadomtsev-Petviashvili (KP) and the Boussinesq (Bo) equations. We present several solutions of these…
In this paper, an efficient algorithm of logarithmic transformation to Hirota bilinear form of the KdV-type bilinear equation is established. In the algorithm, some properties of Hirota operator and logarithmic transformation are…
Applying the inverse scattering transform to study a focusing two-component Hirota equation with nonzero boundary conditions at infinity. Through the spectral problem and the adjoint spectral problem, the analyticity properties and symmetry…
In this paper, we primarily construct Darboux transformation(DT) of the nonlocal coupled modified complex integrable dispersionless (cm-CID) equation, which is first proposed by the connection with a nonlocal coupled modified complex short…
The technique of Darboux transformation is applied to nonlocal partner of two-dimensional periodic A_{n-1} Toda lattice. This system is shown to admit a representation as the compatibility conditions of direct and dual overdetermined linear…
Continuous symmetries of the Hirota difference equation, commuting with shifts of independent variables, are derived by means of the dressing procedure. Action of these symmetries on the dependent variables of the equation is presented.…
A method of integrable discretization of the Liouville type nonlinear partial differential equations is suggested based on integrals. New examples of discrete Liouville type models are presented.
This paper is concerned with a generalized type of Darboux transformations defined in terms of a twisted derivation $D$ satisfying $D(AB)=D(A)+\sigma(A)B$ where $\sigma$ is a homomorphism. Such twisted derivations include regular…
We propose a novel multi-component system of nonlinear equations that generalizes the short pulse (SP) equation describing the propagation of ultra-short pulses in optical fibers. By means of the bilinear formalism combined with a hodograph…
Generalized Euler-Arnold-von Neumann density matrix equations can be solved by a binary Darboux transformation given here in a new form: $\rho[1]=e^{P\ln(\mu/\nu)}\rho e^{-P\ln(\mu/\nu)}$ where $P=P^2$ is explicitly constructed in terms of…
We consider coupled nonlinear Schrodinger equations (CNLSE) which govern the propagation of nonlinear waves in bimodal optical fibers. The nonlinear transform of a dual-frequency signal is used to generate an ultra-short-pulse train. To…
In the recent comment quoted in the title (arXiv:1407.7852v1), a comment is presented on our recent work which derive a generalized nonlinear wave solution formula for mixed coupled nonlinear Sch\"{o}dinger equations by performing the…
The standard binary Darboux transformation is investigated and is used to obtain quasi-Grammian multisoliton solutions of the generalized coupled dispersionless integrable system.
We present a bilinear Hirota representation of the N=2 supersymmetric extension of the Korteweg-de Vries equation. This representation is deduced using binary Bell polynomials, hierarchies and fermionic limits. We, also, propose a new…
A procedure is presented for solving the Fokker-Planck equation with constant diffusion but non-stationary drift. It is based on the correspondence between the Fokker-Planck equation and the non-stationary Schr\"odinger equation. The…