H. J. Shin

Duality in complex sine-Gordon theory

Abstract New aspects of the complex sine-Gordon theory are addressed through the reformulation of the theory in terms of the gauged Wess-Zumino-Witten action. A dual transformation between the theory for the coupling constant β > 0 and the theory for β

Systematic construction of vector solitons

We present a simple but powerful method for constructing multisolitons; of the integrable Manakov (coupled nonlinear Schrodinger) equation. Our method is essentially equivalent to the inverse scattering method (ISM) with the full strength generality but without the mathematical rigor of the ISM. This makes our method appropriate for practical purposes. A closed form of matrix determinant for the N-soliton solution in a nonvanishing background is found in this way. We work out explicitly the two dark vector soliton and the three bright vector soliton cases and demonstrate their novel behaviors.

Higher order nonlinear optical effects on polarized dark solitons

Abstract We extend our previous work on the construction of multi-component dark-type solitons of the vector nonlinear Schrodinger equation to include higher-order nonlinear optical effects. Exact solutions, such as the dark–dark, the bright–dark and the bright–bright pair of solitons are found explicitly and the effects of higher-order nonlinear terms are explained.

Classical matrix sine-Gordon theory

Abstract The matrix sine-Gordon theory, a matrix generalization of the well-known sine-Gordon theory, is studied. In particular, the A3 generalization where fields take values in SU(2) describes integrable deformations of conformal field theory corresponding to the coset SU(2) × SU(2)/SU(2). Various classical aspects of the matrix sine-Gordon theory are addressed. We find exact solutions, solitons and breathers which generalize those of the sine-Gordon theory with internal degrees of freedom, by applying the Zakharov-Shabat dressing method and explaining their physical properties. Infinite current conservation laws and then Backlund transformation of the theory are obtained from the zero curvature formalism of the equation of motion. From the Backlund transformation, we also derive exact solutions as well as a nonlinear superposition principle by making use of Bianchis permutability theorem.

Deformed minimal models and generalized Toda theory

Abstract We introduce a generalization of Ar-type Toda theory based on a non-Abelian group G, which we call the (Ar, G)-Toda theory, and its affine extensions in terms of gauged Wess-Zumino-Witten actions with deformation terms. In particular, the affine (A1, SU(2))-Toda theory describes the integrable deformation of the minimal conformal theory for the critical Ising model by the operator Φ(2,1). We derive infinite conserved charges and soliton solutions from the Lax pair of the affine (A1, SU(2))-Toda theory. Another type of integrable deformation which accounts for the Φ(3,1)-deformation of the minimal model is also found in the gauged Wess-Zumino-Witten context and its infinite conserved charges are given.

Conformal turbulence with boundary

Abstract Based upon the formalism of conformal field theory with a boundary, we give a description of the boundary effect on fully developed two dimensional turbulence. Exact one and two point velocity correlation functions and energy power spectrum confined in the upper half plane are obtained using the image method. This result enables us to address the infrared problem of the theory of conformal turbulence.

Vortex strings and nonabelian sine-Gordon theories

Abstract We generalize the Lund-Regge model for vortex string dynamics in 4-dimensional Minkowski space to the arbitrary n -dimensional case. The n -dimensional vortex equation is identified with a nonabelian sine-Gordon equation and its integrability is proven by finding the associated linear equations of the inverse scattering. An explicit expression of vortex coordinates in terms of the variables of the nonabelian sine-Gordon system is derived. In particular, we obtain the n -dimensional vortex soliton solution of the Hasimoto-type from the one soliton solution of the nonabelian sine-Gordon equation.

Vortex string dynamics in an external antisymmetric tensor field

Abstract We study the Lund–Regge equation that governs the motion of strings in a constant background antisymmetric tensor field by using the duality between the Lund–Regge equation and the complex sine-Gordon equation. Similar to the cases of vortex filament configurations in fluid dynamics, we find various exact solitonic string configurations which are the analogue of the Kelvin wave, the Hasimoto soliton and the smoke ring. In particular, using the duality relation, we obtain a completely new type of configuration which corresponds to the breather of the complex sine-Gordon equation.

Solutions of conformal turbulence on a half plane

Abstract Exact solutions of conformal turbulence restricted to the upper half plane are obtained. We show that the inertial range of homogeneous and isotropic turbulence with constant enstrophy flux develops in a distant region from the boundary. Thus in the presence of an anisotropic boundary, these exact solutions of turbulence generalize Kolmogorovs solution consistently and differ from the Polyakovs bulk case which requires a fine tuning of coefficients. The simplest solution in our case is given by the minimal model of p = 2, q = 33 and moreover we find a fixed point of solutions when p , q become large.

Lund–Regge vortex strings in terms of Weierstrass elliptic functions

Abstract We study quasi-periodic solutions of the Lund–Regge model in terms of the elliptic functions of Weierstrass. They describe the Kida-class motions of relativistic strings in an external antisymmetric tensor field. Our solution includes various vortex string shapes such as the closed vortex ring, the helicoidal filament, the generalized Zees solution and the Hasimoto type 1-soliton filament.