Geodesic

Sommaire du Fascicule no. 1

Foreword
p. 3-4
On the relation between the continuous and discrete Painlev\'e equations
p. 5-22
An elementary approach to the polynomial $\tau$-functions of the KP hierarchy
p. 23-36
A new construction of recursion operators for systems of the hydrodynamic type
p. 37-49
An analogue of the Moutard transformation for the Goursat equation $\theta_{xy}=2\sqrt {\lambda(x,y)\theta_x\theta_y}$
p. 50-57
Existence of a global solution of the Whitham equations
p. 58-71
Nonlinear fourth-order differential equations with solutions in the form of transcendents
p. 72-87
Integrable ordinary differential equations on free associative algebras
p. 88-101
B\"acklund transformations for hyperbolic surfaces in $E^3$ via Weingarten congruences
p. 102-117
Asymptotic approximations for a new eigenvalue in linear problems without a threshold
p. 118-127
Initial boundary value problems for the nonlinear Schr\"odinger equation
p. 128-143
Factoring linear partial differential operators and the Darboux method for integrating nonlinear partial differential equations
p. 144-160

Sommaire du Fascicule no. 2

Foreword
Darboux maps and $\mathcal D$-modules
p. 164-170
Inverse bi-Hamiltonian separable chains
p. 171-181
Quantum integrability and quantum chaos in the micromaser
p. 182-204
Integrable Hamiltonian systems with two degrees of freedom associated with holomorphic functions
p. 205-211
Reduction of bi-Hamiltonian systems and separation of variables: An example from the Boussinesq hierarchy
p. 212-230
A retarded action functional for the Dirac polaron
p. 231-238
Binary Darboux transformations and $N$-wave systems in rings
p. 239-250
Graded Lie algebras, representation theory, integrable mappings, and integrable systems
p. 251-271
Nets, lattices, and multicomponent KP hierarchies
p. 272-283
Applications of Darboux transformations to the self-dual Yang--Mills equations
p. 284-293
Degenerate bi-Hamiltonian structures of the hydrodynamic type
p. 294-304
A quest for the integrable equation in $3+1$ dimensions
p. 305-309
The hyperbolic Heisenberg and sigma models in $1+1$ dimensions
p. 310-320

Sommaire du Fascicule no. 3

In Memory of Boris Valentinovich Medvedev
p. 323-324
Hamiltonian and commutation relations
p. 325-333
Universal Verma modules and $W$-resolvents over Ka\v c--Moody algebras
p. 334-356
Solution of the operator equation $i\varepsilon dy/dt=A(t)y$ on intervals containing turning points
p. 357-371
Fermions in strong external fields in $2+1$ and $1+1$ dimensions
p. 372-384
The $H$ model of critical dynamics: A proof of the multiplicative renormalizability of the simplified $H_0$~model
p. 385-399
The hybrid renormalization
p. 400-416
Nonstationary polaron
p. 417-425
A simplified version of higher covariant derivative regularization
p. 426-434
It is impossible to eliminate gauge degrees of freedom from the exact superpotential for $N_c>N_f$
p. 435-443
The holomorphic effective action in $N$=2 $D$=4 supergauge theories with various gauge groups
p. 444-455
Dispersion of Lagrangian trajectories in a random large-scale velocity field
p. 456-467
The Coleman--Weinberg effective potential in superconductivity theory
p. 468-481
An analytic method in general relativity
p. 482-496