New analytical solutions and modulation instability analysis for the nonlinear (1+1)-dimensional Phi-four model
Boubekeur Gasmi, Armando Ciancio, Alaaeddin Moussa, Lama Alhakim, Yazid Mati
Abstract
Abstract This paper deals with the nonlinear (1+1)-dimensional Phi-four equation in the sense of the Katugampola operator, which can be used to model a variety of real-world applications. To solve this equation, we propose a generalized double auxiliary equation method that yields several new exact solutions. We also use linear stability analysis to discuss the instability modulation analysis for stationary solutions. Other partial differential equations can have their exact solutions found using the proposed methodology.
Topics & Concepts
InstabilityNonlinear systemPartial differential equationOperator (biology)Variety (cybernetics)MathematicsApplied mathematicsModulation (music)Stability (learning theory)Differential equationMathematical analysisComputer sciencePhysicsQuantum mechanicsMachine learningRepressorStatisticsGeneTranscription factorAcousticsChemistryBiochemistryNonlinear Waves and SolitonsNonlinear Photonic SystemsAdvanced Mathematical Physics Problems