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Piecewise smooth localized solutions of Liénard‐type equations with application to NLSE
Author(s) -
Das Prakash Kumar,
Mandal Supriya,
Panja Madan M.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5249
Subject(s) - mathematics , piecewise , mathematical analysis , partial differential equation , nonlinear system , bounded function , type (biology) , domain (mathematical analysis) , ordinary differential equation , differential equation , space (punctuation) , constant (computer programming) , physics , ecology , linguistics , philosophy , quantum mechanics , computer science , biology , programming language
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.