منابع مشابه
Generalized cofactors and nonlinear superposition principles
It is known from Lie’s works that the only ordinary differential equation of first order in which the knowledge of a certain number of particular solutions allows the construction of a fundamental set of solutions is, excepting changes of variables, the Riccati equation. For planar complex polynomial differential systems, the classical Darboux integrability theory exists based on the fact that ...
متن کاملA Class of PDEs with Nonlinear Superposition Principles
Through assuming that nonlinear superposition principles NLSPs are embedded in a Lie group, a class of 3rd-order PDEs is derived from a general determining equation that determine the invariant group. The corresponding NLSPs and transformation to linearize the nonlinear PDE are found, hence the governing PDE is proved C-integrable. In the end, some applications of the PDEs are explained, which ...
متن کاملLinear superposition in nonlinear equations.
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...
متن کاملSuperposition in nonlinear wave and evolution equations
As has been shown recently [Cooper et al. 2002], [Khare et al. 2002a], [Khare et al. 2003], [Khare et al. 2002b] (periodic) Jacobian elliptic functions (if they are solutions of a certain nonlinear wave and evolution equation (NLWEE)) are start solutions for generating new solutions of the NLWEE by a linear superposition procedure. Thus, elliptic functions are of specific importance for finding...
متن کاملLinear Superposition in Nonlinear Wave Dynamics
We study nonlinear dispersive wave systems described by hyperbolic PDE’s in Rd and difference equations on the lattice Zd. The systems involve two small parameters: one is the ratio of the slow and the fast time scales, and another one is the ratio of the small and the large space scales. We show that a wide class of such systems, including nonlinear Schrodinger and Maxwell equations, Fermi–Pas...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1970
ISSN: 0022-247X
DOI: 10.1016/0022-247x(70)90192-7