On hybrid Painleve equations
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Data
2021-02-23
Autores
Alves, Victor Cesar Costa
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Universidade Estadual Paulista (Unesp)
Resumo
A teoria das equações de Painleve é explicada primeiramente no contexto histórico da criação de novas equações a partir da análise de singularidade no plano complexo. O estudo da hierarquia SL (N) mKdV resulta na teoria das equações A(1) Painleve ou das equações de Ince e, naturalmente, suas Transformações Backlund para as reduções correspondentes (coalescência). A teoria da coalescência é então totalmente explorada conectando todas as equações de Ince e Painleve. Com tal formalismo, podemos construir equações híbridas que preservam a propriedade Painleve. Indo além disso, equações deformadas são então desenvolvidas, estendendo as equações mistas.
The theory of Painleve equations is first explained in the historical context of the creation of new equations from the singularity analysis on the complex plane. The study of the SL(N) mKdV hierarchy results in the theory of either the A(1) Painleve equations or the Ince’s equations, and naturally their Backlund Transformations for the corresponding reductions (coalescence). The theory of coalescence is then fully explored connecting all Ince's and Painleve equations. With such a formalism, we are able to construct hybrid equations that preserve the Painleve property. Going beyond that, deformed equations are then developed, extending the mixed equations.
The theory of Painleve equations is first explained in the historical context of the creation of new equations from the singularity analysis on the complex plane. The study of the SL(N) mKdV hierarchy results in the theory of either the A(1) Painleve equations or the Ince’s equations, and naturally their Backlund Transformations for the corresponding reductions (coalescence). The theory of coalescence is then fully explored connecting all Ince's and Painleve equations. With such a formalism, we are able to construct hybrid equations that preserve the Painleve property. Going beyond that, deformed equations are then developed, extending the mixed equations.
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Física matemática, Painleve, Equações de, Solitons