153 research outputs found
Linear Subspaces of Solutions Applied to Hirota Bilinear Equations
- Linear subspace of solution is applied to Boussinesq and Kadomtseve-Petviashvili (KP) equations using Hirota bilinear transformation. A sufficient and necessary condition for the existence of linear subspaces of exponential travelling wave solutions to Hirota bilinear equations is applied to show that multivariate polynomials whose zeros form a vector space can generate the desire Hirota bilinear equations with given linear subspaces of solutions and formulate such multivariate polynomials by using multivariate polynomials which have one and only one zero
A refined invariant subspace method and applications to evolution equations
The invariant subspace method is refined to present more unity and more
diversity of exact solutions to evolution equations. The key idea is to take
subspaces of solutions to linear ordinary differential equations as invariant
subspaces that evolution equations admit. A two-component nonlinear system of
dissipative equations was analyzed to shed light on the resulting theory, and
two concrete examples are given to find invariant subspaces associated with
2nd-order and 3rd-order linear ordinary differential equations and their
corresponding exact solutions with generalized separated variables.Comment: 16 page
An algebro-geometric proof of Witten's conjecture
We present a new proof of Witten's conjecture. The proof is based on the
analysis of the relationship between intersection indices on moduli spaces of
complex curves and Hurwitz numbers enumerating ramified coverings of the
2-sphere.Comment: 12 pages, no figure
Solitons, Tau-functions and Hamiltonian Reduction for Non-Abelian Conformal Affine Toda Theories
We consider the Hamiltonian reduction of the two-loop
Wess-Zumino-Novikov-Witten model (WZNW) based on an untwisted affine Kac-Moody
algebra \cgh. The resulting reduced models, called {\em Generalized
Non-Abelian Conformal Affine Toda (G-CAT)}, are conformally invariant and a
wide class of them possesses soliton solutions; these models constitute
non-abelian generalizations of the Conformal Affine Toda models. Their general
solution is constructed by the Leznov-Saveliev method. Moreover, the dressing
transformations leading to the solutions in the orbit of the vacuum are
considered in detail, as well as the -functions, which are defined for
any integrable highest weight representation of \cgh, irrespectively of its
particular realization. When the conformal symmetry is spontaneously broken,
the G-CAT model becomes a generalized Affine Toda model, whose soliton
solutions are constructed. Their masses are obtained exploring the spontaneous
breakdown of the conformal symmetry, and their relation to the fundamental
particle masses is discussed.Comment: 47 pages. LaTe
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