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Gill’s result [7] applied to Thue equations, yields that the height of the solutions are bounded. [14]) considered the problem to determine effectively all solu- tions of a given
In this section we will apply the Young integral and rough path integral of local time defined in sections 2 and 3 to prove a useful extension to Itˆ o’s formula.. Assume the
We now construct explicitly a piecewise classical solution for Heaviside initial data that satisfies the Rankine-Hugoniot jump conditions (hence it is a weak solution and will be
Key words: orthogonal polynomials; Askey–Wilson polynomials; q-difference equation; three term recurrence; raising operators; lowering operators; root systems; double affine
The third step is recovering of the potential U ( x, t, λ ) and respectively the solution of the nonlinear equation Q ( x, t ) at an arbitrary moment from the scattering data at
This paper presents an explicit form of the action of the intertwining operator on polynomials by use of harmonic and Jacobi polynomials.. It is the symmetry group of the regular 2
Recall that in the general classification problem, once the quasi-exactly solvable Lie algebras of differential operators g are determined, the next step is to construct second
We construct the exact solution of the nonlinear FPE whose coefficients have a special form, and for the coefficients of a general form we construct the leading term of
