Molecules and New Interactional Structures for a (2+1)-Dimensional Generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt Equation

Li, Yan; Yao, Ruoxia; Xia, Yarong

doi:10.1007/s10473-023-0106-7

Cited by 10 publications

(4 citation statements)

References 40 publications

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“…[1][2][3] The exact solution of NLPDEs can describe various physical properties exhibited by the equation, therefore, the search for effective methods of solving NLPDEs has received a lot of attention. Until now, many useful methods have been proposed, such as Darboux transformation, [4,5] Bäcklund transformation, [7] inverse scattering transformation, [8] variable separation method, [9,10] Hirota bilinear method, [11][12][13] etc. Among them, Hirota bilinear method is most studied by many scholars owing to its simplicity and directness.…”

Section: Introductionmentioning

confidence: 99%

Trajectory equation of a lump before and after collision with other waves for generalized Hirota–Satsuma–Ito equation

et al. 2023

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Based on the Hirota bilinear and long wave limit methods, the hybrid solutions of m-lump with n-soliton and n-breather wave for generalized Hirota-Satsuma-Ito (GHSI) equation are constructed. Then, by approximating solutions of the GHSI equation along some parallel orbits at infinity, the trajectory equation of a lump wave before and after collision with n-soliton and n-breather wave are studied, and the expression of phase shift for lump wave before and after collision are given. Furthermore, it is revealed that collisions between the lump wave and other waves are elastic, the corresponding collision diagrams are used to further explain.

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Section: Introductionmentioning

confidence: 99%

Trajectory equation of a lump before and after collision with other waves for generalized Hirota–Satsuma–Ito equation

et al. 2023

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“…Refs. [15][16][17][18][19][20][21][22][23][24][25][26] have considered a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (gKDKK) system in fluid mechanics and plasma physics,…”

Section: Introductionmentioning

confidence: 99%

“…Some hybrid solutions composed of the lumps, breathers and soliton molecules for System (1) have been investigated [25]. Some kinds of interactional structures including the soliton molecule, the breather molecule and the soliton-breather molecule have been constructed [26].…”

Section: Introductionmentioning

confidence: 99%

Bilinear form, Pfaffian, soliton and breather solutions for a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics

Cheng

Tian

Shen

et al. 2022

Preprint

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In this paper, a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics is studied. Bilinear form under certain constraints is given via the Hirota method. The Nth-order Pfaffian solutions are proved via the Pfaffian technique, where N is a positive integer. N-soliton and the higher-order breather solutions are derived from the Nth-order Pfaffian solutions. Y/X-type solitons are constructed via adding some conditions to the N-soliton solutions. Elastic and inelastic interactions between the two solitons are presented graphically. Y/X-type breathers are constructed via adding some conditions to the higher-order breather solutions. Y-type breathers describe the inelastic interactions between the two breathers, and the X-type breathers describe the different two-breather structure. We investigate the influence of the coefficients in the system on those solitons and breathers as follows: the amplitudes of those solitons and breathers are related to l1 and l2; the periods of those breathers are related to l1, l2, l3 and l5, where l1, l2, l3 and l5 are the constant coefficients in the system.

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“…When different parameters are selected for the coefficients a, b, c, d, g and h, equation (1) can be reduced to many classical integrable equations. Here, we present the following examples.When a = b = 1, c = d = g = h = 0 and z = x, equation (1) is reduced to the Korteweg-de Vries (KdV) equation+ When a = 1, b = h 1 , c = h 5 , g = 0, d + h = 0 and z = x, equation(1)is reduced to the (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation[38] …”

mentioning

confidence: 99%

New lump solutions and several interaction solutions and their dynamics of a generalized (3+1)-dimensional nonlinear differential equation

Feng,

Zhao

2024

Commun. Theor. Phys.

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In this paper, we mainly pay attention to prove the existence of lump solutions to a generalized (3+1)-dimensional nonlinear differential equation. Hirota's bilinear method and a quadratic function method are employed to derive the lump solutions localized in the whole plane for a (3+1)-dimensional nonlinear differential equation. Three examples of such nonlinear equation are presented to investigate the exact expressions of the lump solutions. Moreover, the 3d plots and corresponding density plots of the solutions are given to show the space structures of the lump waves. In addition, the breath-wave solutions and several interaction solutions of the (3+1)-dimensional nonlinear differential equation are obtained and their dynamics are analyzed.

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Molecules and New Interactional Structures for a (2+1)-Dimensional Generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt Equation

Cited by 10 publications

References 40 publications

Trajectory equation of a lump before and after collision with other waves for generalized Hirota–Satsuma–Ito equation

Trajectory equation of a lump before and after collision with other waves for generalized Hirota–Satsuma–Ito equation

Bilinear form, Pfaffian, soliton and breather solutions for a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics

New lump solutions and several interaction solutions and their dynamics of a generalized (3+1)-dimensional nonlinear differential equation

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