# Wave Equation with Slowly Decaying Potential: asymptotics of Solution and Wave Operators

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 5, Issue: 4, page 122-149
- ISSN: 0973-5348

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topDenisov, S. A.. "Wave Equation with Slowly Decaying Potential: asymptotics of Solution and Wave Operators." Mathematical Modelling of Natural Phenomena 5.4 (2010): 122-149. <http://eudml.org/doc/197704>.

@article{Denisov2010,

abstract = {In this paper, we consider one-dimensional wave equation with real-valued square-summable
potential. We establish the long-time asymptotics of solutions by, first, studying the
stationary problem and, second, using the spectral representation for the evolution
equation. In particular, we prove that part of the wave travels ballistically if
q ∈ L2(ℝ+) and this result is
sharp.},

author = {Denisov, S. A.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {wave equation; square-summable potential; wave operators; one space dimension; long-time asymptotics; spectral representation},

language = {eng},

month = {5},

number = {4},

pages = {122-149},

publisher = {EDP Sciences},

title = {Wave Equation with Slowly Decaying Potential: asymptotics of Solution and Wave Operators},

url = {http://eudml.org/doc/197704},

volume = {5},

year = {2010},

}

TY - JOUR

AU - Denisov, S. A.

TI - Wave Equation with Slowly Decaying Potential: asymptotics of Solution and Wave Operators

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/5//

PB - EDP Sciences

VL - 5

IS - 4

SP - 122

EP - 149

AB - In this paper, we consider one-dimensional wave equation with real-valued square-summable
potential. We establish the long-time asymptotics of solutions by, first, studying the
stationary problem and, second, using the spectral representation for the evolution
equation. In particular, we prove that part of the wave travels ballistically if
q ∈ L2(ℝ+) and this result is
sharp.

LA - eng

KW - wave equation; square-summable potential; wave operators; one space dimension; long-time asymptotics; spectral representation

UR - http://eudml.org/doc/197704

ER -

## References

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- P. Lax, R. Phillips. Scattering theory. Pure and Applied Mathematics, Academic Press Inc., Boston, 1989. Zbl0697.35004
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- B. Simon. Orthogonal polynomials on the unit circle. Parts 1 and 2. American Mathematical Society Colloquium Publications, American Mathematical Society, Providence, 2005.
- B. Simon. Some Schrödinger operators with dense point spectrum. Proc. Amer. Math. Soc., 125 (1997), 203–208. Zbl0888.34071

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