## What is integrability? |

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### Contents

Why Are Certain Nonlinear PDEs Both Widely Applicable | 1 |

Survey of Model Equations | 19 |

Envoi | 56 |

Copyright | |

20 other sections not shown

### Common terms and phrases

action-angle variables algorithm amplitude analogous analytic arbitrary asymptotic C-integrable Cauchy problem change of variables coefficients commuting conservation laws conserved density consider constants contact transformations coordinate corresponding defined degenerative dispersion laws dependent variable derivatives differential equations dynamical Eckhaus example exist expansion finite number follows formal symmetry formula function n(A Hamiltonian Hirota equations holomorphic Im{D inequalities infinite infinity integrability conditions integrable equations integrable systems KdV equation KP equation Laurent series Lax pair Lemma Lie algebra linear equation mapping Math method model equation NLS equation nondegenerative nonlinear evolution equations nonlinear evolution PDEs nonlinear PDEs nontrivial Note obtained operator Painleve parameter PDEs phase space Phys poles polynomial potential q(x reduced reflectionless potentials rescaling resonant surface right-hand side satisfy scattering matrix Sect Shabat singular soliton solution solvable substitution Theorem theory values vanish vector wave Weyl function zero