In this work, the rapidly convergent approximation method (RCAM) followed by appropriate modifications is applied to obtain piecewise smooth solutions and conserved quantities of a Liénard‐type equation and some important nonlinear partial differential equations reducible to former one. Explicit parameter dependence of the solution has been sensibly used to determine parameter dependence of the constant of the motion as well as the domain in the parameter space for which the piecewise smooth solution is bounded. Solution of Liénard‐type equation is then used to find piecewise smooth traveling wave solutions and corresponding conserved quantities of nonlinear Schrödinger equation. These findings affirm the efficiency of the RCAM for analytical exercise of variety of nonlinear systems of ordinary/partial differential equations appear as mathematical model of physical processes.

This article deals with the evaluation of some integrals involving error-, exponential-and algebraic functions with an objective to derive explicit expressions for the second and third order correction terms in the approximation of the modified error function, playing important role in the study of Stefan problem. The results obtained here appear to be new and resolve the lack of desired monotonicity property in the results presented by Ceretania et al. [1]. Results derived here seem to be useful for the researchers working with Stefan problems.

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In this work, a principle for getting heteroclinic orbit of a dynamical system has been proposed when the solution is known in a compact form. The proposed principle has been tested through its application to a three species Lotka-Volterra system, which may appear as a mathematical model of human pathogen system. The domain in parameter ( , ) space involve in the model, and the region of initial condition ℍ = {( (0), (0), (0)) ∈ ℝ 3 } ⊂ ℝ 3 for the existence of heteroclinic orbit have been derived.

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