Forward scattering for non-linear wave propagation in (3 + 1)-dimensional Jimbo-Miwa equation using singular manifold and group transformation methods
Ahmed S. Rashed, S. M. Mabrouk, Abdul–Majid Wazwaz
Abstract
Forward scattering of (3 + 1)-dimensional Jimbo-Miwa (JM) equation is investigated by singular manifold method (SMM). The detected Lax pair is reduced through three parameters group method into a compatible couple of ordinary differential equations (ODEs). Three forms of symmetry variables have been discussed leading to integrable system of ODEs. Some new closed form solutions have been obtained. The three parameters group method, which is rarely used in solving PDEs, has emphasized its efficiency in creating symmetry solutions of evolution equations.
Topics & Concepts
OdeMathematical analysisMathematicsOrdinary differential equationInverse scattering transformGroup (periodic table)Partial differential equationSymmetry (geometry)Integrable systemLax pairSymmetry groupManifold (fluid mechanics)Separation of variablesTransformation (genetics)Differential equationMathematical physicsFirst-order partial differential equationPhysicsQuantum mechanicsGeometryMechanical engineeringChemistryEngineeringBiochemistryGeneNonlinear Waves and SolitonsNonlinear Photonic SystemsAlgebraic structures and combinatorial models