Partial Differential Equations and Solitary Waves Theory

By Abdul-Majid Wazwaz. 2009

1,192 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f32f9419a952fea215f7342f3596d19056a2aee3

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Citations in the corpus

Stationary solutions for nonlinear dispersive Schrödinger’s equation (2011, background): “The theory of nonlinear evolution equations (NLEEs) has made a tremendous amount of progress in the past couple of decades [1–10].”
Application of variational iteration method for Hamilton–Jacobi–Bellman equations (2013, background): “In fact, the VIM demonstrates fast convergence of the solution and therefore provides several significant advantages [48].”
On The Exact Solution of Newell-Whitehead-Segel Equation Using the Homotopy Perturbation Method (2011, neutral): “…method is applied to solve the nonlinear non-homogeneous partial differential equations (He, 2005; Yildirim, 2009; He, 2006; He, 2006; He, 2006; He, 2005; He, 1998; He, 1998; He, 1999; He, 1999; He, 2000; He, 2006; He, 2005; He, 2005; He, 2005; Koçak et al., 2011; Gepreel, 2011; Cao and…”
A study on the systems of the Volterra integral forms of the Lane–Emden equations by the Adomian decomposition method (2014, methodology): “But we can readily solve this problem by means of solution continuation or convergence acceleration techniques, such as analytic continuation [39], the diagonal Padé approximants [5, 26], the iterated Shanks transform [26], Adomian’s asymptotic decomposition method [25, 26, 40] and the higher-order ”
Finding exact solutions of nonlinear PDEs using the natural decomposition method (2017, methodology): “(5.10) is given by v.x, t/ D 4c 3 cos 2 x ct 4 , jx ctj 2 0, otherwise (5.18) The exact solution is in closed agreement with the result obtained by ADM [1].”