Computation of homoclinic solutions to periodic orbits in a reduced water-wave problem
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Publication:675942
DOI10.1016/S0167-2789(96)00206-0zbMath0888.34040WikidataQ126351698 ScholiaQ126351698MaRDI QIDQ675942
Gabriel J. Lord, Alan R. Champneys
Publication date: 12 March 1997
Published in: Physica D (Search for Journal in Brave)
Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Numerical methods for ordinary differential equations (65L99)
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Uses Software
Cites Work
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- Weakly non-local solitons for capillary-gravity waves: Fifth-degree Korteweg-de Vries equation
- Existence of perturbed solitary wave solutions to a model equation for water waves
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- A theory of solitary water-waves in the presence of surface tension
- Solitary waves with surface tension. I: Trajectories homoclinic to periodic orbits in four dimensions
- Hopf's bifurcation theorem and the center theorem of Liapunov with resonance cases
- Hamiltonian long-wave approximations to the water-wave problem
- \(N\)-pulse homoclinic orbits in perturbations of resonant Hamiltonian systems
- Hunting for homoclinic orbits in reversible systems: A shooting technique
- Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system
- Bifurcation of a plethora of multi-modal homoclinic orbits for autonomous Hamiltonian systems
- Exact solitary water waves with capillary ripples at infinity
- The Numerical Computation of Connecting Orbits in Dynamical Systems
- Nonlinearly Resonant Surface Waves and Homoclinic Bifurcation
- A plethora of solitary gravity-capillary water waves with nearly critical Bond and Froude numbers
- Numerical Computation and Continuation of Invariant Manifolds Connecting Fixed Points
- Water waves for small surface tension: an approach via normal form
- Reversible Diffeomorphisms and Flows
- The cusp horseshoe and its bifurcations in the unfolding of an inclination-flip homoclinic orbit
- Rate of convergence of numerical approximations to homoclinic bifurcation points
- Weakly Nonlocal Solitary Waves in a Singularly Perturbed Korteweg–De Vries Equation
- NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS
- NUMERICAL COMPUTATIONS OF CONNECTING ORBITS IN DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
- NUMERICAL ANALYSIS AND CONTROL OF BIFURCATION PROBLEMS (II): BIFURCATION IN INFINITE DIMENSIONS
- PERIODIC AND HOMOCLINIC ORBITS IN A TWO-PARAMETER UNFOLDING OF A HAMILTONIAN SYSTEM WITH A HOMOCLINIC ORBIT TO A SADDLE-CENTER
- Optimization in Bifurcation Problems using a Continuation Method
- Weakly Nonlocal Solitary Waves in a Singularly Perturbed Nonlinear Schrödinger Equation
- On Short‐Scale Oscillatory Tails of Long‐Wave Disturbances
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