Browsing by Author "CHAU, LL"

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AN ALTERNATIVE EXPLICIT CONSTRUCTION OF N-SOLITON SOLUTIONS IN 1+1 DIMENSIONS
(1991-07-01)
CHAU, LL
;
SHAW, JC
;
YEN, HC
;
應用數學系
;
Department of Applied Mathematics
Using the special Riemann-problem technique of Zakharov et al. [Sov. Phys. JETP 47, 1017 (1978)], an explicit N-step Backlund transformation is derived for a class of 1 + 1-dimensional nonlinear evolution equations, thus providing an alternative explicit expression of their N-soliton solutions which no longer involves computations of the intermediate solutions, nor leaves any expansion of N x N determinants (and their differentiation) to be done.
N-SOLITON-TYPE SOLUTIONS OF SU(2) SELF-DUALITY YANG-MILLS EQUATIONS IN VARIOUS SPACES AND THEIR BACKLUND-TRANSFORMATIONS
(1994-11-07)
CHAU, LL
;
SHAW, JC
;
YEN, HC
;
應用數學系
;
Department of Applied Mathematics
We show that Getmanov's N-soliton-type solutions in the self-duality Yang-Mills (SDYM) equations in the (+---)-signatured M4-space can be derived in a unified way similar to that of deriving 't Hooft's instanton solutions in the (++++)-signatured E4-space. Further, we show that such N-soliton-type solutions can also be constructed for the SDYM equations in the (+-+-)-signatured real D4-space.
SOLVING THE KP HIERARCHY BY GAUGE TRANSFORMATIONS
(1992-10-01)
CHAU, LL
;
SHAW, JC
;
YEN, HC
;
應用數學系
;
Department of Applied Mathematics
We show that it is convenient to use "gauge" transformations (sometimes called explicit Backlund transformations) to generate new solutions for the KP hierarchy. Two particular kinds of gauge transformation operators, constructed out of the initial wave functions, are of fundamental importance in this approach. Through such gauge transformations, a very simple formula for the tau-function is obtained, encompassing and unifying all kinds of existing solutions. The corresponding free fermion representation and Baker functions for the new tau function can also be constructed.