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A multiple exp-function method for nonlinear differential equations and its application
Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics (math-ph)
2010/11/10
A multiple exp-function method to exact multiple wave solutions of nonlinear partial differential equations is proposed. The method is oriented towards ease of use and capability of computer algebra s...
On certain new integrable second order nonlinear differential equations and their connection with two dimensional Lotka-Volterra system
arbitrary parameters integrable cases
2010/4/1
In this paper, we consider a second order nonlinear ordinary differential equation of the form
$\ddot{x}+k_1\frac{\dot{x}^2}{x}+(k_2+k_3x)\dot{x}+k_4x^3+k_5x^2+k_6x=0$, where $k_i$'s, $i=1,2,...,6,$...
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...
Bounds for Asymptote Singularities of Certain Nonlinear Differential Equations
Bounded operator Comparison methods Generalized Emden-Fowler equations Nonlinear differential equations Vertical asymptote
2008/7/2
Bounds for Asymptote Singularities of Certain Nonlinear Differential Equations.
MULTIPLE POSITIVE SOLUTIONS TO BVPS FOR HIGHER ORDER NONLINEAR DIFFERENTIAL EQUATIONS IN BANACH SPACES
Multiple positive solutions h
2007/12/10
In this article, the author employs the conical expansion and compression fixed point principle and the fixed point index theory to show that there exist at least two positive solutions for a higher o...
Oscillation Criteria for Second Order Nonlinear Differential Equations with Damping
Oscillation averaging damping Riccati substitution second order
2010/3/1
Oscillation criteria are given for second order nonlinear differential equations with damping of the form (a(t) y (x ) \dot x)\dot{}+ p(t) \dot x + q (t) f (x ) = 0,\quad t\geq t0, where p and q are a...