Numerical Methods for Nonlinear Waves


  1. J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems (SIAM, Philadelphia, 2010). Erratum
  2. J. Yang, "Newton-Conjugate-Gradient Methods for Solitary Wave Computations", J. Comp. Phys. 228, 7007–7024 (2009).
  3. J. Yang, "Iteration methods for stability spectra of solitary waves", J. Comp. Phys. 227, 6862-6876 (2008).
  4. J. Yang and T.I. Lakoba, "Accelerated Imaginary-time Evolution Methods for the Computation of Solitary Waves", Stud. Appl. Math. 120, 265-292 (2008) (arXiv:0711.3434v1 [nlin.PS])
  5. T.I. Lakoba and J. Yang, "A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity", J. Comp. Phys. 226, 1668-1692 (2007).
  6. T.I. Lakoba and J. Yang, "A mode elimination technique to improve convergence of iteration methods for finding solitary waves", J. Comp. Phys. 226, 1693-1709 (2007).
  7. J. Yang and T.I. Lakoba, "Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations", Stud. Appl. Math. 118, 153-197 (2007).
  8. Z. Musslimani and J. Yang, "Self-trapping of light in a two-dimensional periodic structure." J. Opt. Soc. Am. B. 21, 973-981 (2004) [This paper contains a modification of the Petviashvili method].
  9. J. Yang, "Internal oscillations and instability characteristics of (2+1) dimensional solitons in a saturable nonlinear medium." Phys. Rev. E. 66, 026601 (2002) [This paper uses the shooting method to determine solitons and their stable and unstable eigenvalues].


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