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Exact Solutions to the Six-Vertex Model with Domain Wall Boundary Conditions and Uniform Asymptotics of Discrete Orthogonal Polynomials on an Infinite Lattice
Statistical Mechanics Random Matrices Orthogonal Polynomials Asymptotics Riemann-Hilbert Problems
2015/1/19
In this dissertation the partition function, $Z_n$, for the six-vertex model with domain wall boundary conditions is solved in the thermodynamic limit in various regions of the phase diagram. In the f...
Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations
Analysis of PDEs (math.AP) Exactly Solvable and Integrable Systems (nlin.SI)
2010/11/11
We first review the known mathematical results concerning the KP type equations. Then we perform numerical simulations to analyze various qualitative properties of the equations : blow-up versus long ...
Smooth soliton solutions of a new integrable equation by Qiao
Exactly Solvable and Integrable Systems (nlin.SI) Mathematical Physics(math-ph) Analysis of PDEs(math.AP) Pattern Formation and Solitons(nlin.PS)
2010/11/10
We find a transformation which relates a new third-order integrable nonlinear evolution equation, introduced recently by Qiao, with the well-known modified Korteweg - de Vries equation. Then we use th...
Non-isoparametric solutions of the eikonal equation
Non-isoparametric solutions eikonal equation
2010/12/3
In this paper, we prove that a quartic solution of the eikonal equation |∇xf|2 = 16x6 in Rn is either isoparametric or congruent to a polynomial f = (Pn i=1 x2 i )2 − 8(Pk i=1 x2 i )(Pn
i...