Numerical approximation of solitary waves of the Benjamin equation
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[1] Qiang Du,et al. Computing the Ground State Solution of Bose-Einstein Condensates by a Normalized Gradient Flow , 2003, SIAM J. Sci. Comput..
[2] Jerry L. Bona,et al. A Boussinesq system for two-way propagation of nonlinear dispersive waves , 1998 .
[3] T. Benjamin. Solitary and periodic waves of a new kind , 1996, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.
[4] Werner C. Rheinboldt,et al. Numerical continuation methods: a perspective , 2000 .
[5] Jianke Yang,et al. Nonlinear Waves in Integrable and Nonintegrable Systems , 2010, Mathematical modeling and computation.
[6] Mechthild Thalhammer,et al. A minimisation approach for computing the ground state of Gross-Pitaevskii systems , 2009, J. Comput. Phys..
[7] E. Hairer,et al. Geometric Numerical Integration , 2022, Oberwolfach Reports.
[8] Boris A. Malomed,et al. EMBEDDED SOLITONS IN SECOND-HARMONIC-GENERATING SYSTEMS , 1999 .
[9] Gene H. Golub,et al. Matrix computations , 1983 .
[10] Taras I. Lakoba,et al. Accelerated Imaginary‐time Evolution Methods for the Computation of Solitary Waves , 2007, 0711.3434.
[11] J. Boyd. Deleted Residuals, the QR-Factored Newton Iteration, and Other Methods for Formally Overdetermined Determinate Discretizations of Nonlinear Eigenproblems for Solitary, Cnoidal, and Shock Waves , 2002 .
[12] Hannu Olkkonen,et al. Computation of Hilbert Transform via Discrete Cosine Transform , 2010, J. Signal Inf. Process..
[13] E. Hairer,et al. Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems , 1993 .
[14] V. A. Dougalis,et al. Numerical Solution of Some Nonlocal, Nonlinear Dispersive Wave Equations , 2000, J. Nonlinear Sci..
[15] Jon Wilkening,et al. Computation of Time-Periodic Solutions of the Benjamin–Ono Equation , 2008, J. Nonlinear Sci..
[16] John P. Boyd,et al. Comparison of three spectral methods for the Benjamin-Ono equation: Fourier pseudospectral, rational Christov functions and Gaussian radial basis functions , 2011 .
[17] T. Benjamin. Internal waves of permanent form in fluids of great depth , 1967, Journal of Fluid Mechanics.
[18] Jianke Yang,et al. Newton-conjugate-gradient methods for solitary wave computations , 2009, J. Comput. Phys..
[19] Felipe Linares,et al. On generalized Benjamin type equations , 2004 .
[20] T. Lakoba,et al. Universally‐Convergent Squared‐Operator Iteration Methods for Solitary Waves in General Nonlinear Wave Equations , 2007, nlin/0702033.
[21] Gilbert Strang,et al. The Discrete Cosine Transform , 1999, SIAM Rev..
[22] V. Petviashvili. Equation of an extraordinary soliton , 1976 .
[23] Dmitry Pelinovsky,et al. Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationary Solutions of Nonlinear Wave Equations , 2004, SIAM J. Numer. Anal..
[24] E. Hairer,et al. Solving Ordinary Differential Equations II , 2010 .
[25] L. Einkemmer. Structure preserving numerical methods for the Vlasov equation , 2016, 1604.02616.
[26] T. Benjamin. A new kind of solitary wave , 1992, Journal of Fluid Mechanics.
[27] E. Hairer,et al. Solving Ordinary Differential Equations I , 1987 .
[28] E. Hairer,et al. Geometric Numerical Integration: Structure Preserving Algorithms for Ordinary Differential Equations , 2004 .
[29] Juan M. Restrepo,et al. Solitary-Wave Solutions of the Benjamin Equation , 1999, SIAM J. Appl. Math..
[30] John P. Boyd,et al. Numerical and perturbative computations of solitary waves of the Benjamin-Ono equation with higher order nonlinearity using Christov rational basis functions , 2012, J. Comput. Phys..
[31] A. Durán,et al. A Numerical Study of the Stability of Solitary Waves of the Bona–Smith Family of Boussinesq Systems , 2007, J. Nonlinear Sci..
[32] M. Ablowitz,et al. Spectral renormalization method for computing self-localized solutions to nonlinear systems. , 2005, Optics letters.
[33] Stephen A. Martucci,et al. Symmetric convolution and the discrete sine and cosine transforms , 1993, IEEE Trans. Signal Process..
[34] J. Sanz-Serna,et al. Accuracy and conservation properties in numerical integration: the case of the Korteweg-de Vries equation , 1997 .
[35] John P. Boyd,et al. Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm , 2022 .
[36] John P. Boyd,et al. Solitons from sine waves: analytical and numerical methods for non-integrable solitary and cnoidal waves , 1986 .
[37] Taras I. Lakoba,et al. A mode elimination technique to improve convergence of iteration methods for finding solitary waves , 2007, J. Comput. Phys..
[38] Víctor M. Pérez-García,et al. Optimizing Schrödinger Functionals Using Sobolev Gradients: Applications to Quantum Mechanics and Nonlinear Optics , 2001, SIAM J. Sci. Comput..
[39] Taras I. Lakoba,et al. A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity , 2007, J. Comput. Phys..
[40] Jerry L. Bona,et al. Models for internal waves in deep water , 1999 .