Multiscale Approach to Parabolic Equations Derivation: Beyond the Linear Theory

[1]  James Corones,et al.  Bremmer series that correct parabolic approximations , 1975 .

[2]  Fred D. Tappert,et al.  The parabolic approximation method , 1977 .

[3]  A. V. Popov,et al.  A generalization of the parabolic equation of diffraction theory , 1977 .

[4]  Vimal Singh,et al.  Perturbation methods , 1991 .

[5]  R. Ibrahim Book Reviews : Nonlinear Oscillations: A.H. Nayfeh and D.T. Mook John Wiley & Sons, New York, New York 1979, $38.50 , 1981 .

[6]  Jon F. Claerbout,et al.  Fundamentals of Geophysical Data Processing: With Applications to Petroleum Prospecting , 1985 .

[7]  A. P. Kiselev,et al.  Gaussian beams at large distances , 1986 .

[8]  Michael D. Collins,et al.  Generalization of the split‐step Padé solution , 1994 .

[9]  W. Kuperman,et al.  Computational Ocean Acoustics , 1994 .

[10]  Gary S. Brown,et al.  Parabolic equation formulation via a singular perturbation technique and its application to scattering from irregular surfaces , 1998 .

[11]  A. D. Zakharenko,et al.  A direct multiple-scale approach to the parabolic equation method , 2012 .

[12]  Gadi Fibich,et al.  The Nonlinear Schrödinger Equation: Singular Solutions and Optical Collapse , 2015 .

[13]  Pavel S. Petrov Three-dimensional iterative parabolic approximations , 2015 .

[14]  Matthias Ehrhardt,et al.  Wide-angle parabolic approximations for the nonlinear Helmholtz equation in the Kerr media , 2016 .

[15]  Matthias Ehrhardt,et al.  Transparent boundary conditions for iterative high-order parabolic equations , 2016, J. Comput. Phys..