Skip to main content

10 Result(s)

within Jerry L. Bona Remove this filter

and

  1. No Access

    Article

    Convergence of periodic wavetrains in the limit of large wavelength

    The Korteweg-de Vries equation was originally derived as a model for unidirectional propagation of water waves. This equation possesses a special class of traveling-wave solutions corresponding to surface soli...

    Jerry L. Bona in Applied Scientific Research (1981)

  2. No Access

    Article

    Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation

    Certain generalizations of one of the classical Boussinesq-type equations, $$u_{tt} = u_{xx} - (u^2 + u_{xx} )_{xx} $$ ...

    Jerry L. Bona, Robert L. Sachs in Communications in Mathematical Physics (1988)

  3. No Access

    Article

    A model system for strong interaction between internal solitary waves

    A mathematical theory is mounted for a complex system of equations derived by Gear and Grimshaw that models the strong interaction of two-dimensional, long, internal gravity waves propagating on neighboring py...

    Jerry L. Bona, Gustavo Ponce, Jean-Claude Saut… in Communications in Mathematical Physics (1992)

  4. No Access

    Chapter and Conference Paper

    Continuous evolution of functions and measures toward fixed points of contraction map**s

    Let T be a contraction map** on an appropriate Banach space B(X). Then the evolution equation y t =T y −

    Jerry L. Bona, Edward R. Vrscay in Fractals in Engineering (2005)

  5. No Access

    Article

    Long Wave Approximations for Water Waves

    In this paper, we obtain new nonlinear systems describing the interaction of long water waves in both two and three dimensions. These systems are symmetric and conservative. Rigorous convergence results are pr...

    Jerry L. Bona, Thierry Colin, David Lannes in Archive for Rational Mechanics and Analysis (2005)

  6. No Access

    Article

    Dispersive blow-up II. Schrödinger-type equations, optical and oceanic rogue waves

    Addressed here is the occurrence of point singularities which owe to the focusing of short or long waves, a phenomenon labeled dispersive blow-up. The context of this investigation is linear and nonlinear, str...

    Jerry L. Bona, Jean-Claude Saut in Chinese Annals of Mathematics, Series B (2010)

  7. No Access

    Article

    Preface

    Jerry L. Bona, Lokenath Debnath, Henrik Kalisch… in Analysis and Mathematical Physics (2012)

  8. No Access

    Article

    Stability of Solitary-Wave Solutions of Systems of Dispersive Equations

    The present study is concerned with systems $$\begin{aligned} \left\{ \begin{array}{ll} &{} \frac{\partial u}{\partial t} +\frac{\part...

    Jerry L. Bona, Hongqiu Chen, Ohannes Karakashian in Applied Mathematics & Optimization (2017)

  9. No Access

    Article

    Finite Element Methods for a System of Dispersive Equations

    The present study is concerned with the numerical approximation of periodic solutions of systems of Korteweg–de Vries type, coupled through their nonlinear terms. We construct, analyze and numerically validate...

    Jerry L. Bona, Hongqiu Chen, Ohannes Karakashian… in Journal of Scientific Computing (2018)

  10. No Access

    Article

    Numerical Study of the Second-Order Correct Hamiltonian Model for Unidirectional Water Waves

    Second-order correct versions of the usual KdV–BBM models for unidirectional propagation of long-crested, surface water waves are considered here. The class of models studied here has a Hamiltonian structure a...

    Jerry L. Bona, Hongqiu Chen, Youngjoon Hong, Ohannes Karakashian in Water Waves (2019)