2010
DOI: 10.1515/zna-2010-1008
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Odd-Soliton-Like Solutions for the Variable-Coefficient Variant Boussinesq Model in the Long Gravity Waves

Abstract: Under investigation in this paper, with symbolic computation, is a variable-coefficient variant Boussinesq (vcvB) model for the nonlinear and dispersive long gravity waves travelling in two horizontal directions with varying depth. Connection between the vcvB model and a variable-coefficient Broer-Kaup (vcBK) system is revealed under certain constraints. By means of the N-fold Darboux transformation for the vcBK system, odd-soliton-like solutions in terms of the Vandermonde-like determinant for the vcvB model … Show more

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Cited by 39 publications
(5 citation statements)
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References 18 publications
(23 reference statements)
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“…Relevant issues can be seen in refs. [24][25][26]. Note that the parameters α and β are real constants (we will take α = 1 and β = 2 as examples in all the following analysis), while the wave numbers a 1 and a 2 are arbitrary complex constants.…”
Section: IImentioning
confidence: 99%
“…Relevant issues can be seen in refs. [24][25][26]. Note that the parameters α and β are real constants (we will take α = 1 and β = 2 as examples in all the following analysis), while the wave numbers a 1 and a 2 are arbitrary complex constants.…”
Section: IImentioning
confidence: 99%
“…Through the similar analysis to expressions (20) and (21), we could also derive that the interaction among the three solitons is elastic. Relevant issues can also be seen in [58][59][60][61][62]. (a) a 0 = 2, λ = 0.05, q 1 = 1, q 1 = 1, 1 = −1, 1 = 0, q 2 = 0.5, q 2 = 0, 2 = −2, 2 = 0, q 3 = 1, q 3 = 0, 3 = 10, and 3 = 0; (b) a 0 = 2, λ = 0.05, q 1 = 1, q 1 = 0, 1 = −1, 1 = 1, q 2 = 0.8, q 2 = 0.8, 2 = −5, 2 = 0, q 3 = 1.5, q 3 = −1.5, 3 = 20, F and 3 = 0…”
Section: Soliton Interaction Propertiesmentioning
confidence: 99%
“…In the next section, with symbolic computation [34][35][36][37][38][39], (a) we will firstly apply the Darboux transformation (DT) to derive the bright one-and two-soliton solutions for System (1); (b) through the asymptotic analysis for the two-soliton solution, energy-exchange soliton collisions with partial or complete energy exchange will be examined; (c) the first three conservation laws for System (1) will be obtained. At last, the conclusions will be addressed in Sect.…”
Section: Introductionmentioning
confidence: 99%