Periodic solutions of nonlinear equations obtained by linear superposition
نویسندگان
چکیده
منابع مشابه
Periodic Solutions of Nonlinear Equations Obtained by Linear Superposition
We show that a type of linear superposition principle works for several nonlinear differential equations. Using this approach, we find periodic solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear Schrödinger (NLS) equation, the λφ4 model, the sine-Gordon equation and the Boussinesq equation by making appropriate linear superpositions of known periodic solutions. This unusual pr...
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We find new periodic solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear Schrödinger (NLS) equation, the λφ4 model, the sine-Gordon equation and the Boussinesq equation by making appropriate linear superpositions of known periodic solutions. This unusual procedure for generating solutions of nonlinear differential equations is successful as a consequence of some powerful, recen...
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Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of so...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2002
ISSN: 0305-4470
DOI: 10.1088/0305-4470/35/47/309