The patterns of traveling wave on shallow water modeled by Green-Naghdi equation [PDF]
MATEC Web of Conferences, 2022 The Green-Naghdi equations are a shallow water waves model which play important roles in nonlinear wave fields. By using the trial equation method and the Complete discrimination system for the polynomial we obtained the classification of travelling wave
Wei Haitong
doaj +1 more source
Chiral Solitons with Bohm Potential by Modified Simple Equation Method and Trial Equation Scheme
Acta Physica Polonica A, 2018 In this paper we obtain soliton solutions to chiral nonlinear Schrodinger's equation with the Bohm potential by the modified simple equation method and trial equation method. Solitons and shock wave solutions are obtained. Additionally, singular periodic solutions are revealed as a by-product of these approaches and these are also listed. The existence
Belic, M. +5 more
openaire +3 more sources
Mesh-based numerical implementation of the localized boundary-domain integral equation method to a variable-coefficient Neumann problem [PDF]
, 2005 An implementation of the localized boundary-domain integral-equation (LBDIE) method for the numerical solution of the Neumann boundary-value problem for a second-order linear elliptic PDE with variable coefficient is discussed.
Mikhailov, SE, Nakhova, IS
core +6 more sources
Propagation of solitons in optical fibers with generalized Kudryashov’s refractive index
Results in Physics, 2021 The propagation of optical solitons in optical fibers with the generalized Kudryashov’s refractive index is described by a high order nonlinear Schrödinger equation.
Fan Sun
doaj +1 more source
Deterministic numerical solutions of the Boltzmann equation using the fast spectral method [PDF]
, 2013 The Boltzmann equation describes the dynamics of rarefied gas flows, but the multidimensional nature of its collision operator poses a real challenge for its numerical solution. In this paper, the fast spectral method [36], originally developed by Mouhot
White, Craig +4 more
core +4 more sources
Solitary-wave solutions of the Degasperis-Procesi equation by means of the homotopy analysis method [PDF]
, 2010 The homotopy analysis method is applied to the Degasperis-Procesi equation in order to find analytic approximations to the known exact solitary-wave solutions for the solitary peakon wave and the family of solitary smooth-hump waves.
Abbasbandy, S., Parkes, E.J.
core +4 more sources
Results in Physics, 2022 This paper secures exact solutions from perturbed complex Ginzburg–Landau equation that is taken into account with Kerr law and cubic–quintic–septic nonlinearity.
Ming-Yue Wang
doaj +1 more source
Stabilization of the trial method for the Bernoulli problem in case of prescribed Dirichlet data [PDF]
, 2013 We apply the trial method for the solution of Bernoulli’s free boundary problem when the Dirichlet boundary condition is imposed for the solution of the underlying Laplace equation and the free boundary is updated according to the Neumann boundary ...
Giannoula Mitrou +3 more
core +1 more source
Variational Principles for Two Compound Nonlinear Equations with Variable Coefficients [PDF]
Journal of Applied and Computational Mechanics, 2021 It is very important to seek explicit variational principles for nonlinear partial differential equations, which are theoretical bases for many methods to solve or analyze the nonlinear phenomena and problems.
Xiao-Qun Cao +4 more
doaj +1 more source
Trial methods for Bernoulli's free boundary problem [PDF]
, 2014 Free boundary problems deal with solving partial differential equations in a domain, a part of whose boundary is unknown – the so-called free boundary. Beside the standard boundary conditions that are needed in order to solve the partial differential ...
Mitrou, Giannoula
core +1 more source