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A comparative study of approximate symmetry and approximate homotopy symmetry to a class of perturbed nonlinear wave equations is performed. First, complete infinite-order approximate symmetry classification of the equation is obtained by means of the method originated by Fushchich and Shtelen. An optimal system of one-dimensional subalgebras is derived and used to construct general formulas of approximate...
In this paper, we study the global existence and the asymptotic behavior of the solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects (E){ψt=−(1−α)ψ−θx+αψxx,θt=−(1−α)θ+νψx+(ψθ)x+αθxx, with initial data (I)(ψ,θ)(x,0)=(ψ0(x),θ0(x))→(ψ±,θ±)as x→±∞, where α and ν are positive constants such that α<1, ν<α(1−α). Through constructing...
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