## Nonlinear and Modern Mathematical Physics: Proceedings of the First International WorkshopThe volume is very beneficial to both starting and experienced researchers working in the field of integrable nonlinear equations, soliton theory, and nonlinear waves. It will be an excellent reference book for graduate students majoring in mathematical physics and engineering sciences. This volume covers a broad range of current interesting topics in nonlinear and modern mathematical physics, and reviews recent developments in integrable systems, soliton theory and nonlinear dynamics. The book is suitable for both starting and experienced researchers working in nonlinear sciences, and it is a good reference for students of mathematical, physical and engineering sciences. |

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### Contents

Optical Switching with Longrange Interactions between Strongly | 28 |

Singular Solutions of Nonlinear Systems and Patterns Associated with | 43 |

Integral Transformation and Darboux Transformation of Heuns | 58 |

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### Common terms and phrases

2+l)-dimensional 2010 American Institute 2DKK AKNS asymptotic line-solitons bilinear form China coefficients commutative condition constant corresponding Darboux transformation defined denote derived differential operator discrete edited by W. X. eigenfunction evolution equations exact solutions extended KP flows given global attractor Grassmannian Hamiltonian structures Heun's differential equation Hidden Central System integrable couplings integrable equations integrable systems International Workshop edited invariant KdV equation KP equation KP hierarchy lattice equation Lax operator Lax pairs Lemma Lett Lie algebras linear loop algebra Math matrix method Modern Mathematical Physics multi-component non-isospectral noncommutative nonlinear Nonlinear and Modern obtained parameters partial differential equations Phys polynomials Proposition pseudo-differential operators q-KP Q. P. Liu reduction resonance satisfies Sato semiflow soliton equations soliton solutions spectral problem super supersymmetric susy T-function Theorem theory variables variational identity vector field Virasoro Virasoro constraints Volterra lattice X. B. Hu zero curvature equation Zhang