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Physics Letters A, 1974
Abstract The non-linear Miura transformation, which converts the N -soliton solution of the modified KdV equation into an N -soliton solution for the KdV equation itself, is related to an unitary transformation of the operators associated with these equations.
T.L. Perelman +2 more
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Abstract The non-linear Miura transformation, which converts the N -soliton solution of the modified KdV equation into an N -soliton solution for the KdV equation itself, is related to an unitary transformation of the operators associated with these equations.
T.L. Perelman +2 more
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Mathematical Notes, 1994
We consider the following system of nonlinear evolution equations: \[ \begin{aligned} \dot b_n & = b_n\Biggl(c_1(b_{n+ 1}- b_{n- 1})- c_2\Biggl(b_{n+ 1} \Biggl(\sum^2_{k= 0} b_{n+ k}\Biggr)- b_{n- 1} \Biggl(\sum^2_{k= 0} b_{n+ k}\Biggr)\Biggr)\Biggr),\tag{1}\\ b_n & = b_n(t),\quad t\in [0, T),\quad n\in \mathbb{Z};\quad c_1, c_2\in \mathbb{C};\;\cdot =
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We consider the following system of nonlinear evolution equations: \[ \begin{aligned} \dot b_n & = b_n\Biggl(c_1(b_{n+ 1}- b_{n- 1})- c_2\Biggl(b_{n+ 1} \Biggl(\sum^2_{k= 0} b_{n+ k}\Biggr)- b_{n- 1} \Biggl(\sum^2_{k= 0} b_{n+ k}\Biggr)\Biggr)\Biggr),\tag{1}\\ b_n & = b_n(t),\quad t\in [0, T),\quad n\in \mathbb{Z};\quad c_1, c_2\in \mathbb{C};\;\cdot =
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Applied Mechanics and Materials, 2012
It is difficult to obtain exact solutions of the nonlinear partial differential equations (PDEs) due to the complexity and nonlinearity, especially for non-integrable systems. In this case, some reasonable approximations of real physics are considered, by means of the standard truncated expansion approach to solve real nonlinear system is proposed.
Jiang Long Wu, Wei Rong Yang
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It is difficult to obtain exact solutions of the nonlinear partial differential equations (PDEs) due to the complexity and nonlinearity, especially for non-integrable systems. In this case, some reasonable approximations of real physics are considered, by means of the standard truncated expansion approach to solve real nonlinear system is proposed.
Jiang Long Wu, Wei Rong Yang
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2019
Some recent results concerning nonlinear non-Abelian KdV and mKdV equations are presented. Operator equations are studied in references [2]-[7] where structural properties of KdV type equations are investigated. Now, in particular, on the basis of results, the special finite dimensional case of matrix soliton equations is addressed to: solutions of ...
Sandra Carillo +2 more
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Some recent results concerning nonlinear non-Abelian KdV and mKdV equations are presented. Operator equations are studied in references [2]-[7] where structural properties of KdV type equations are investigated. Now, in particular, on the basis of results, the special finite dimensional case of matrix soliton equations is addressed to: solutions of ...
Sandra Carillo +2 more
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The European Physical Journal B, 2006
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Wei, Guang-Mei +3 more
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Wei, Guang-Mei +3 more
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Spectral approach to Korteweg-de Vries equations on the compactified real line
Applied Numerical Mathematics, 2022Christian Klein, Nikola Stoilov
exaly