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Related papers: Interaction properties of complex mKdV solitons

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The Hirota equation and the Sasa-Satsuma equation are U(1)-invariant integrable generalizations of the modified Korteweg-de Vries equation. These two generalizations admit oscillatory solitons, which describe harmonically modulated complex…

Exactly Solvable and Integrable Systems · Physics 2016-09-09 Stephen C. Anco , Abdus Sattar Mia , Mark R. Willoughby

Harmonically modulated complex solitary waves which are a generalized type of envelope soliton (herein coined oscillatory solitons) are studied for the two U(1)-invariant integrable generalizations of the modified Korteweg-de Vries…

Exactly Solvable and Integrable Systems · Physics 2016-09-09 Stephen C. Anco , Abdus Sattar Mia , Mark R. Willoughby

By constructing the general six-parameter bright two-soliton solution of the integrable coupled nonlinear Schrodinger equation (Manakov model) using the Hirota method, we find that the solitons exhibit certain novel inelastic collision…

solv-int · Physics 2009-10-30 R. Radhakrishnan , M. Lakshmanan , J. Hietarinta

We consider the soliton solutions of a recently proposed coupled Sasa-Satsuma-mKdV equation using the Kadomtsev-Petviashvili reduction method. The system consists of a complex-valued component coupled with a real-valued one. Under zero or…

Exactly Solvable and Integrable Systems · Physics 2026-03-20 Changyan Shi , Bao-Feng Feng

The KdV-Sawada-Kotera equation has single-, two- and three-soliton solutions. However, it is not known yet whether it has N-soliton solutions for any N. Viewing it as a perturbed KdV equation, the asymptotic expansion of the solution is…

Exactly Solvable and Integrable Systems · Physics 2008-12-03 Yair Zarmi

Acoustic solitons obtained through a reductive perturbation scheme are normally governed by a Korteweg-de Vries (KdV) equation. In multispecies plasmas at critical compositions the coefficient of the quadratic nonlinearity vanishes.…

Plasma Physics · Physics 2019-01-23 Frank Verheest , Willy A. Hereman

Interaction of two solitons of the different polarities in the framework of modified Korteweg-de Vries (mKdV) equation is studied. Three types of soliton interaction are considered: exchange and overtaking for solitons of the same polarity,…

Atmospheric and Oceanic Physics · Physics 2015-06-22 E. N. Pelinovsky , E. G. Shurgalina

In this paper, we are concerned with various soliton solutions to the coupled Hirota equation, as well as to the Sasa-Satsuma equation which can be viewed as one reduction case of the coupled Hirota equation. First, we derive bright-bright,…

Exactly Solvable and Integrable Systems · Physics 2025-02-19 Changyan Shi , Bingyuan Liu , Bao-Feng Feng

The N=2 supersymmetric KdV equation of Inami and Kanno is bilinearized employing the Hirota method and the existence of $N$ soliton solutions is demonstrated. The exact form of the solutions are explicitly obtained and an interesting…

Exactly Solvable and Integrable Systems · Physics 2009-11-07 Sasanka Ghosh , Debojit Sarma

The novel dynamical features underlying soliton interactions in coupled nonlinear Schr{\"o}dinger equations, which model multimode wave propagation under varied physical situations in nonlinear optics, are studied. In this paper, by…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 T. Kanna , M. Lakshmanan

We investigate the interaction of solitons with an external periodic field within the framework of the modified Korteweg-de Vries (mKdV) equation. In the case of small perturbation a simple dynamical system is used to describe the soliton…

Pattern Formation and Solitons · Physics 2025-03-11 Marcelo V. Flamarion , Efim Pelinovsky , Ioann Melnikov

We derive the equations governing the motion of Kerr solitons in pair waveforms. Recent experiments in microresonators have studied a variety of interaction effects in multisoliton waveforms, including collisions and formation of soliton…

Pattern Formation and Solitons · Physics 2025-07-11 Amir Leshem , Sanzida Akter , Logan Courtright , Pradyoth Shandilya , Curtis R. Menyuk , Omri Gat

Numerical experiments involving the interaction of two solitary waves of the ion acoustic plasma equations are described. An exact 2-soliton solution of the relevant KdV equation was fitted to the initial data, and good agreement was…

solv-int · Physics 2009-10-31 Yi Li , D. H. Sattinger

In this paper, we study the formation of solitons, their propagation and collision behaviour in an integrable multicomponent (2+1)-dimensional long wave-short wave resonance interaction ($M$-LSRI) system. First, we briefly revisit our…

Pattern Formation and Solitons · Physics 2015-12-04 T Kanna , K Sakkaravarthi , M Vijayajayanthi , M Lakshmanan

Bright plane soliton solutions of an integrable (2+1) dimensional ($n+1$)-wave system are obtained by applying Hirota's bilinearization method. First, the soliton solutions of a 3-wave system consisting of two short wave components and one…

Exactly Solvable and Integrable Systems · Physics 2009-11-13 T. Kanna , M. Vijayajayanthi , K. Sakkaravarthi , M. Lakshmanan

We study the dynamics of soliton solutions to the perturbed mKdV equation $\partial_t u = \partial_x(-\partial_x^2 u -2u^3) + \epsilon V u$, where $V\in \mathcal{C}^1_b(\mathbb{R})$, $0<\epsilon\ll 1$. This type of perturbation is…

Analysis of PDEs · Mathematics 2011-11-01 Quanhui Lin

There has been found an exact solution of the mixed problem for Shrodinger's compact U(m)-vector nonlinear model with an arbitrary sign of the coupling constant. It is shown, that in case of m>2 there is a new class of solutions - mixed…

Exactly Solvable and Integrable Systems · Physics 2009-11-07 A. M. Agalarov , R. M. Magomedmirzaev

Wecritically review the recent progress in understanding soliton propagation in birefringent optical fibers.By constructing the most general bright two-soliton solution of the integrable coupled nonlinear Schroedinger equation (Manakov…

Exactly Solvable and Integrable Systems · Physics 2019-08-17 M. Lakshmanan , T. Kanna , R. Radhakrishnan

This paper presents a complete description of the interaction of two solitons with nearly equal speeds for the quartic (gKdV) equation. By constructing an approximate solution of the problem, we prove that at the main order, the two…

Analysis of PDEs · Mathematics 2009-11-02 Yvan Martel , Frank Merle

We consider KdV-type equations with $C^1$ nonhomogeneous nonlinearities and small dispersion $\varepsilon$. The first result consists in the conclusion that, in the leading term with respect to $\varepsilon$, the solitary waves in this…

Analysis of PDEs · Mathematics 2015-12-01 Georgy Omel'yanov
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