An extended Petviashvili method for the numerical generation of traveling and localized waves

作者: Jorge Álvarez , Angel Durán

DOI: 10.1016/J.CNSNS.2013.12.004

关键词:

摘要: Abstract A family of fixed-point iterations is proposed for the numerical computation traveling waves and localized ground states. The methods are extended versions Petviashvili type, they applicable when nonlinear term system contains homogeneous functions different degree. described applied to several examples interest, that calibrate their efficiency.

参考文章(17)
John P Boyd, Chebyshev and Fourier spectral methods Boyd. ,(2001)
Dmitry E. Pelinovsky, Yury A. Stepanyants, Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationary Solutions of Nonlinear Wave Equations SIAM Journal on Numerical Analysis. ,vol. 42, pp. 1110- 1127 ,(2004) , 10.1137/S0036142902414232
Isaías Alonso-Mallo, Angel Durán, Nuria Reguera, Simulation of coherent structures in nonlinear Schrödinger-type equations Journal of Computational Physics. ,vol. 229, pp. 8180- 8198 ,(2010) , 10.1016/J.JCP.2010.07.018
Jianke Yang, Newton-conjugate-gradient methods for solitary wave computations Journal of Computational Physics. ,vol. 228, pp. 7007- 7024 ,(2009) , 10.1016/J.JCP.2009.06.012
Hai Yen Nguyen, Frédéric Dias, A Boussinesq system for two-way propagation of interfacial waves Physica D: Nonlinear Phenomena. ,vol. 237, pp. 2365- 2389 ,(2008) , 10.1016/J.PHYSD.2008.02.020
Jianke Yang, Taras I. Lakoba, Accelerated Imaginary‐time Evolution Methods for the Computation of Solitary Waves Studies in Applied Mathematics. ,vol. 120, pp. 265- 292 ,(2008) , 10.1111/J.1467-9590.2008.00398.X
Weizhu Bao, Qiang Du, Computing the Ground State Solution of Bose--Einstein Condensates by a Normalized Gradient Flow SIAM Journal on Scientific Computing. ,vol. 25, pp. 1674- 1697 ,(2004) , 10.1137/S1064827503422956