相关论文: Extreme Superposition: High-Order Fundamental Rogu…
We study the fundamental rogue wave solutions of the focusing nonlinear Schr\"odinger equation in the limit of large order. Using a recently-proposed Riemann-Hilbert representation of the rogue wave solution of arbitrary order $k$, we…
General rogue waves of infinite order constitute a family of solutions of the focusing nonlinear Schr\"odinger equation that have recently been identified in a variety of asymptotic limits such as high-order iteration of B\"acklund…
This paper is devoted to a comprehensive analysis of a family of solutions of the focusing nonlinear Schr\"odinger equation called general rogue waves of infinite order. These solutions have recently been shown to describe various limit…
The integrable focusing nonlinear Schrodinger equation admits soliton solutions whose associated spectral data consist of a single pair of conjugate poles of arbitrary order. We study families of such multiple-pole solitons generated by…
We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schr\"{o}dinger equations. Based on the generalized Darboux transformation and formal series method, we obtain the high-order rogue wave solution without the…
Using the generalised nonlinear Schr\"odinger equation, we investigate how the effect of third-order dispersion, self-steepening, and Raman-induced-self-frequency shift have an impact on the higher-order rogue waves. We observe that…
We show that the same special solution of the focusing nonlinear Schr\"{o}dinger equation that has been shown to arise in a certain near-field/large-order limit from soliton and Peregrine-like rogue wave solutions actually arises…
In this work, we analyze the asymptotic behaviors of high-order rogue wave solutions with multiple large parameters and discover novel rogue wave patterns, including claw-like, OTR-type, TTR-type, semi-modified TTR-type, and their modified…
The higher-order dispersive and nonlinear effects (alias {\it the perturbation terms}) like the third-order dispersion, the self-steepening, and the self-frequency shift play important roles in the study of the ultra-short optical pulse…
We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schr\"{o}dinger equations. We find four fundamental rogue waves can emerge for second-order vector RW in the coupled system, in contrast to the high-order ones…
The long wave-short wave model describes the interaction between the long wave and the short wave. Exact higher-order rational solution expressed by determinants is calculated via the Hirota's bilinear method and the KP hierarchy reduction.…
We analyze the large-$n$ behavior of soliton solutions of the integrable focusing nonlinear Schr\"odinger equation with associated spectral data consisting of a single pair of conjugate poles of order $2n$. Starting from the zero…
This paper studies highly oscillatory solutions to a class of systems of semilinear hyperbolic equations with a small parameter, in a setting that includes Klein--Gordon equations and the Maxwell--Lorentz system. The interest here is in…
General high-order rogue waves in the nonlinear Schroedinger equation are derived by the bilinear method. These rogue waves are given in terms of determinants whose matrix elements have simple algebraic expressions. It is shown that the…
General higher order rogue waves of a vector nonlinear Schrodinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method. The Nth order semi-rational solutions containing 3N free…
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…
This paper investigates the asymptotic behavior of high-order vector rogue wave (RW) solutions of the coupled nonlinear Schr\"odinger (CNLS) equation in the presence of multiple large internal parameters. We report several new high-order RW…
We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schr\"odinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe…
In this paper, novel rogue wave patterns in the nolocal nonlinear Schr\"odinger equation (NLS) are investigated by means of asymptotic analysis, including heart-pentagon, oval-trangle, and fan-trangle. It is demonstrated that when multiple…
Modulation instability, rogue wave and spectral analysis are investigated for the nonlinear Schrodinger equation with the higher-order terms. The modulation instability distribution characteristics from the sixth-order to the eighth-order…