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Exact, multiple soliton solutions of the double sine Gordon equation
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1978Exact, particular solutions of the double sine Gordon equation in n dimensional space are constructed. Under certain restrictions these solutions areNsolitons, whereN≤ 2q— 1 andqis the dimensionality of spacetime. The method of solution, known as the base equation technique, relates solutions of nonlinear partial differential equations to solutions of ...
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M-component nonlinear evolution equations: multiple soliton solutions
Physica Scripta, 2010Four M-component nonlinear evolution equations, namely the M-component Korteweg–de Vries (KdV) equation, the M-component Kadomtsev–Petviashvili (KP) equation, the M-component modified KdV (mKdV) equation and the M-component mKdV–KP equation, are examined for complete integrability.
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Multiple Soliton Solutions of the High Order Broer–Kaup Equations
Communications in Theoretical Physics, 2000Using the extended homogeneous balance method, which is very concise and primary, we find the multiple soliton solutions of the high order Broer–Kaup equations. The method can be generalized to dealing with high-dimensional Broer–Kaup equations and other class of nonlinear equations.
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Static and stationary multiple soliton solutions to the Einstein equations
Journal of Mathematical Physics, 1985The application of the Belinsky–Zakharov solution-generating technique, i.e., the inverse scattering method, to generate stationary axially symmetric solutions to the vacuum Einstein equations is reduced to a single quadrature when the seed solution is diagonal. The possibility of having real odd-number soliton solutions is investigated.
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Multiple-soliton solutions for coupled KdV and coupled KP systems
Canadian Journal of Physics, 2009In this work we study two systems of coupled KdV and coupled KP equations. The Hirota bilinear method is applied to show that these two systems are completely integrable. Multiple-soliton solutions and multiple singular-soliton solutions are derived for each system. The resonance phenomenon is examined as well.
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Nonlinear Dynamics, 2016
We investigate two Boussinesq equations where the fourth-order terms come with minus and plus signs. We show that the Boussinesq equation with minus fourth-order term gives multiple soliton solutions, whereas the model with the plus fourth-order term gives multiple complex soliton solutions.
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We investigate two Boussinesq equations where the fourth-order terms come with minus and plus signs. We show that the Boussinesq equation with minus fourth-order term gives multiple soliton solutions, whereas the model with the plus fourth-order term gives multiple complex soliton solutions.
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Multiple-soliton solutions for the fifth order Caudrey–Dodd–Gibbon (CDG) equation
Applied Mathematics and Computation, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Some new multiple-soliton solutions of high-dimensional nonlinear wave equations
1991Summary: By using the base-equation technique and the transformation relations to get new solutions of the base equations, we obtain some new multiple- soliton solutions of \(n+1\) dimensional nonlinear wave equations. Gibbon et al. pointed out that the number of solitons in the multi-soliton solutions is constrained by \(N\leq2n+1\).
Lou, Senyue +2 more
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Single and multiple-soliton solutions for the (2+1)-dimensional KdV equation
Applied Mathematics and Computation, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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