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Exact solutions for periodic and solitary matter waves in nonlinear lattices
Exact solutions periodic solitary matter waves nonlinear lattices
2010/12/28
We produce three vast classes of exact periodic and solitonic solutions to the one-dimensional
Gross-Pitaevskii equation (GPE) with the pseudopotential in the form of a nonlinear lattice (NL),induced...
Symmetry analysis and exact solutions of semilinear heat flow in multi-dimensions
Symmetry analysis exact solutions semilinear heat flow in multi-dimensions
2010/11/24
A symmetry group method is used to obtain exact solutions for a semilinear radial heat equation in $n>1$ dimensions with a general power nonlinearity. The method involves an ansatz technique to solve...
Lie group classifications and exact solutions for time-fractional Burgers equation
Lie group classifications exact solutions
2010/11/22
Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests a fractional Lie group method for fractional partial differential equations. A time-f...
A systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variable $x$ and the tempor...
More common errors in finding exact solutions of nonlinear differential equations. I
nonlinear differential equations common errors
2010/4/7
In the recent paper by Kudryashov [Commun. Nonlinear Sci. Numer. Simulat., 2009, V.14, 3507-3529] seven common errors in finding exact solutions of nonlinear differential equations were listed and dis...
Lax pairs, Painlevé properties and exact solutions of the alogero Korteweg-de Vries equation and a new (2+1)-dimensional equation
Lax pairs Painlevé properties exact solutions the alogero Korteweg-de Vries equation
2010/11/1
We prove the existence of a Lax pair for the Calogero Korteweg-de Vries (CKdV) equation. Moreover, we modify the T operator in the the Lax pair of the CKdV equation, in the search of a (2+1)-dimensio...