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  • 1
    Digitale Medien
    Digitale Medien
    C-integrable nonlinear PDEs. II (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2703-2717 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: A technique to perform a convenient Change of (independent) variables in a PDE is reported, and it is used to generate C-integrable nonlinear PDEs, i.e., nonlinear PDEs solvable by an appropriate Change of variables. Several examples of such PDEs are exhibited.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.529112
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  • 2
    Digitale Medien
    Digitale Medien
    Lax pairs galore (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 72-74 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: A formula that yields an (apparently—but only apparently—nontrivial) Lax pair for any nonlinear evolution PDE in 1+1 dimensions possessing a local conservation law is presented. Several examples are exhibited.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.529096
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  • 3
    Digitale Medien
    Digitale Medien
    The evolution partial differential equation ut=uxxx+3(uxxu2 +3u2xu)+3uxu4 (1987)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 538-555 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: The evolution equation ut=uxxx+3(uxxu2 +3u2xu)+3uxu4, u=u(x,t), is integrable; it can be (exactly) linearized by an appropriate change of (dependent) variable. Hence several explicit solutions of the partial differential equation (PDE) can be exhibited; some of them display a remarkable solitronic phenomenology.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.527639
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  • 4
    Digitale Medien
    Digitale Medien
    C-Integrable nonlinear partial differential equations in N+1 dimensions (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1257-1271 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: Two techniques are introduced, which are suitable to manufacture C-integrable nonlinear PDEs (i.e., nonlinear PDEs solvable by an appropriate Change of variables) in N+1 dimensions. Several examples are exhibited.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.529973
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  • 5
    Digitale Medien
    Digitale Medien
    C-integrable nonlinear partial differentiation equations. I (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 875-887 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: A technique to generate C-integrable nonlinear partial differentiation equations (PDEs) (i.e., nonlinear PDEs linearizable by an appropriate Change of variables) is reported, and several examples of such PDEs are exhibited.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.529346
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  • 6
    Digitale Medien
    Digitale Medien
    Universality and integrability of the nonlinear evolution PDE's describing N-wave interactions (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 28-40 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: The universality of the equations describing N-wave interactions is demonstrated by deriving them from a very large class of nonlinear evolution equations (essentially all those whose linear part is dispersive). Various forms of these equations are displayed. The fact that these "universal'' nonlinear evolution equations obtain, by an appropriate asymptotic limit, from such a large class of nonlinear evolution equations, suggests that they should be integrable; since for this it is sufficient that the large class from which they are obtainable contain just one integrable equation. This expectation is validated in several cases, by deriving the equations from known integrable equations. In this manner an explanation may be provided of the (already known) integrable nature of certain equations; and new integrable equations may be obtained. Both S-integrable and C-integrable equations are discussed, namely both equations integrable via an appropriate spectral transform and solvable via an appropriate change of variables. In this paper the treatment is limited to equations in 1+1 dimensions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.528585
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  • 7
    Digitale Medien
    Digitale Medien
    The Burgers equation on the semiline with general boundary conditions at the origin (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 99-105 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: A technique is given to solve the initial/boundary value problem for the Burgers equation ut(x,t)=uxx(x,t)+2 ux(x,t) u(x,t) on the semiline 0≤x〈∞, with the general boundary condition at the origin H[u(0,t),ux(0,t);t]=0. Here "to solve'' means "to reduce to an equation in one variable only.'' This equation is generally nonlinear and integrodifferent ial; it comes in several (equivalent) avatars, which contain nontrivially a free parameter, whose value can be assigned arbitrarily since the solution of the equation is independent of it. In the special case when H(y,z;t)=a(t)y+b(t)(z+y2) −F(t), which is the case relevant for most applications, the equations reduce to linear integral equations of Volterra type, which can in fact be solved by quadratures if a(t)/F(t)=c1 and b(t)/F(t)=c2 are time-independent.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.529101
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  • 8
    Digitale Medien
    Digitale Medien
    Solutions of certain integrable nonlinear PDE's describing nonresonant N-wave interactions (1989)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 30 (1989), S. 639-654 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: The evolution equations that describe, in appropriately "coarse-grained'' and "slow'' variables, the evolution of the envelopes of N nonresonant dispersive waves, can be reduced to the "universal'' form (∂/∂t+vn ∂/∂x) un(x,t) =un(x,t) ∑Nm=1βnmum(x,t). In this paper the special case with βnm=(vm−vn) βm, which is integrable by quadratures, is investigated. The subclass of localized solutions (i.e., vanishing as x→±∞) gives rise to a novel solitonic phenomenology. The class of solutions that are asymptotically finite contains a richer solitonic phenomenology, including those of novel type (which move with the speeds vn, and can have any shape) and more standard kinks (which can move with any speed, and have standard shapes). The class of rational solutions, and the integrable dynamical systems naturally associated with these solutions, are also investigated; these dynamical systems include, and extend, known integrable systems. In this paper the treatment is confined to 1+1 dimensions; at the end, together with some other generalizations, a partially solvable multidimensional extension is reported.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.528432
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  • 9
    Digitale Medien
    Digitale Medien
    Partially solvable quantum many-body problems in D-dimensional space (D=1,2,3,...) (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4208-4226 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: A simple technique employed almost three decades ago to manufacture partially solvable quantum many-body problems is revisited. [A quantum problem is "partially solvable" if (only) some of its eigenvalues and eigenfunctions can be exhibited]. The models thereby generated are characterized by Hamiltonians of normal form, i.e., standard kinetic plus momentum-independent potential energy; in most cases the latter features three-body, in addition to two-body and one-body, interactions. The setting refers to D-dimensional space; the examples focus on D=1, D=2, and D≥2, and include generalizations of, and additional results on, cases recently discussed in the literature, as well as new models. © 1999 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.532961
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  • 10
    Digitale Medien
    Digitale Medien
    Solvable (nonrelativistic, classical) n-body problems on the line. I (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 5659-5670 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: Several solvable n-body problems on the line are exhibited. They are characterized by equations of motion of Newtonian type, mjx¨j=Fj, j=1,...,n, with the "forces'' Fj given as explicit functions of the "particle coordinates'' xk and their velocities x(overdot)k, k=1,...,n; the forces Fj generally also depend on some free parameters, so that in each case there is actually a class of solvable models. In this paper the emphasis is on translation-invariant models, and on values of n sufficiently small ("few-body problems'') to allow the display of the solution of the initial-value problem in completely explicit form.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.530276
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