Exact solutions of a fifth - order Korteweg–de Vries –type equation modeling nonlinear long waves in several natural phenomena
Елена Николова, Mila Chilikova–Lubomirova, Nikolay K. Vitanov
Abstract
In this study we discuss existence of solitary wave solutions of a famous higher-order model evolution equation arising from the water wave theory. This evolution equation describes several nonlinear natural phenomena such as propagation of long waves in shallow water over a flat surface or propagation of long gravity-capillary waves. We obtain several exact analytical solutions of this equation by applying a particular case of the Simplest Equations Method (SEsM).Numerical simulations of the obtained solutions include various kinds of solitary waves depending on a key model parameter.
Topics & Concepts
Korteweg–de Vries equationNonlinear systemKondratiev waveType (biology)Waves and shallow waterWave propagationPhysicsMathematical analysisClassical mechanicsMathematicsMechanicsOpticsGeologyThermodynamicsPaleontologyQuantum mechanicsNonlinear Waves and SolitonsAdvanced Mathematical Physics ProblemsNonlinear Photonic Systems