Related papers: Construction of Nth-order rogue wave solutions for…
We mainly investigate a coupled system of the generalized nonlinear Schr\"odinger equation and the Maxwell-Bloch equations which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order effects including the…
In this paper, we propose the existence and discuss the properties of rogue quantum gravitational waves. More specifically, we numerically solve the Schr\"odinger-Newton system of equations using a spectral scheme with a $4^{th}$ order…
Lump solutions are analytical rational function solutions localized in all directions in space. We analyze a class of lump solutions, generated from quadratic functions, to nonlinear partial differential equations. The basis of success is…
We present exact rational solution for a modified nonlinear Schr$\ddot{o}$dinger equation that takes into account quintic nonlinearity and nonlinear dispersion corrections to the cubic nonlinearity, which could be used to describe rogue…
By employing a mapping to classical anharmonic oscillators, we explore a class of solutions to the Nonlinear Schrodinger Equation (NLSE) in 1+1 dimensions and, by extension, asymptotically in general dimensions. We discuss a possible way…
We establish a bilinear framework for elliptic soliton solutions which are composed by the Lam\'e-type plane wave factors. $\tau$ functions in Hirota's form are derived and vertex operators that generate such $\tau$ functions are presented.…
A generalization of determinant formulas for the classical solutions of Painlev\'e XXXIV and Painlev\'e II equations are constructed using the technique of Darboux transformation and Hirota's bilinear formalism. It is shown that the…
The (2+1)-dimensional [(2+1)d] Fokas system is a natural and simple extension of the nonlinear Schrodinger equation. (see eq. (2) in A. S. Fokas, Inverse Probl. 10 (1994) L19-L22). In this letter, we introduce its PT -symmetric version,…
We use Hirota's method formulated as a recursive scheme to construct complete set of soliton solutions for the affine Toda field theory based on an arbitrary Lie algebra. Our solutions include a new class of solitons connected with two…
In this paper, we calculate the region of emergence of rogue waves in the Sasa-Satsuma equation by performing Penrose stability analysis. We consider Wigner-transformed Sasa-Satsuma equation and separate out unstable solutions, namely…
In the present investigation, the solutions on the periodic and double-periodic background are successfully constructed by Darboux transformation using a plane wave seed solution. Firstly, the Darboux transformation for the…
This paper presents a double spatio-temporal localized Dirac-delta solution for the linear wave equation. The solution arises from the interference of sinusoidal waves with frequencies that vary as a function of the time of emission. It is…
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…
Based on the bilinear operator and symbol calculation, some lump solutions are presented, rationally localized in all directions in the space, to a reduced (3+1)-dimensional KP equation. The lump solutions all contain six parameters, four…
In this paper, we study the novel nonlinear wave structures of a (2+1)-dimensional variable-coefficient Korteweg-de Vries (KdV) system by its analytic solutions. Its $N$-soliton solution are obtained via Hirota's bilinear method, and in…
In this paper, by considering the potential application in two mode nonlinear waves in nonlinear fibers under a certain case, we define a coupled nonlinear Schr\"odinger equation(called Frobenius NLS equation) including its Lax pair.…
In the present paper, we are concerned with the general localized solutions for the complex short pulse equation including soliton, breather and rogue wave solutions. With the aid of a generalized Darboux transformation, we construct the…
We construct breather and rogue wave solutions of a variable coefficient nonlinear Schr\"odinger equation with an external linear potential. This generalized model describes the nonlinear wave propagation in an inhomogeneous plasma/medium.…
Based on the symbolic computation approach, multiple rogue wave solutions of the generalized (2+1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili equation are studied. As an example, we present the 1-rogue wave solutions, 3-rogue wave…
A prototypical example of a rogue wave structure in a two-dimensional model is presented in the context of the Davey-Stewartson~II (DS~II) equation arising in water waves. The analytical methodology involves a Taylor expansion of an…