Korteweg‐devries equation and generalizations. VI. methods for exact solution

Method for Solving the Korteweg-deVries Equation

1967 • 4,326 citations

Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States

1965 • 3,810 citations

XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves

1895 • 3,767 citations

Integrals of nonlinear equations of evolution and solitary waves

1968 • 2,945 citations

Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons

1971 • 2,843 citations

Quantum Mechanics (Non-Relativistic Theory)

1958 • 2,421 citations

Propagation of Ion-Acoustic Solitary Waves of Small Amplitude

1966 • 1,954 citations

The partial differential equation u_t + uu_x = μ_xx

1950 • 1,758 citations

On a quasi-linear parabolic equation occurring in aerodynamics

1951 • 1,655 citations

Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion

1968 • 939 citations

Korteweg-de Vries Equation and Generalizations. I. A Remarkable Explicit Nonlinear Transformation

1968 • 891 citations

On the determination of a differential equation from its spectral function

1987 • 724 citations

Korteweg-de Vries equation: A completely integrable Hamiltonian system

1972 • 565 citations

Reductive Perturbation Method in Nonlinear Wave Propagation. I

1968 • 535 citations

Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation

1969 • 515 citations

On the equations of motion for mixtures of liquid and gas bubbles

1968 • 473 citations

Reflectionless Transmission through Dielectrics and Scattering Potentials

1956 • 325 citations

The Exact N-Soliton Solution of the Korteweg-de Vries Equation

1972 • 199 citations

Korteweg-deVries Equation and Generalizations. V. Uniqueness and Nonexistence of Polynomial Conservation Laws

1970 • 196 citations

A Synergetic Approach to Problems of Nonlinear Dispersive Wave Propagation and Interaction††This paper is dedicated to Professor L. Biermann on his sixtieth birthday. I would like to express my gratitude to Professor Biermann and his Institute of Astrophysics of the Max-Planck-Institute for Physics and Astrophysics for the support they gave to the International School of Nonlinear Mathematics and Physics held in Munich during the summer of 1966.

1967 • 185 citations

Weakly non-linear waves in rotating fluids

1970 • 138 citations

Kinetic Equation for Solitons

1971 • 119 citations

Solitons and Bound States of the Time-Independent Schrödinger Equation

1968 • 109 citations

The decay of the continuous spectrum for solutions of the Korteweg-deVries equation

1973 • 95 citations

Similarity in the asymptotic behavior of collision-free hydromagnetic waves and water waves

2011 • 88 citations

Certain Explicit Relationships between Phase Shift and Scattering Potential

1953 • 43 citations

Asymptotic Theory of Unsteady Three-Dimensional Waves in a Channel of Arbitrary Cross Section

1969 • 41 citations

On the N-tuple Wave Solutions of the Korteweg-de Vries Equation

1972 • 36 citations

NONLINEAR EVOLUTION OF DISTURBANCES IN PLASMAS AND OTHER DISPERSIVE MEDIA.

1966 • 34 citations

Nonlinear Lattice Dynamics and Energy Sharing

1969 • 27 citations