Tian, Lixin Wavelet approximate inertial manifold in nonlinear solitary wave equation. (English) Zbl 0973.35169 J. Math. Phys. 41, No. 8, 5773-5792 (2000). Summary: This paper studies the dynamical behavior of a weakly damped forced Korteweg-de Vries (KdV) equation in a wavelet basis and introduces the wavelet approximate inertial manifold as well as the wavelet Galerkin solution of weakly damped forced KdV equation. The results include theorems that for the KdV equation the wavelet approximate inertial manifold (WAIM) exists and sets up the wavelet Galerkin method of the equation. Error estimates are given by using the WAIM. Cited in 2 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 37L25 Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems 41A30 Approximation by other special function classes 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems Keywords:Korteweg-de Vries equation; error estimates; wavelet approximate inertial manifold; wavelet Galerkin solution PDFBibTeX XMLCite \textit{L. Tian}, J. Math. Phys. 41, No. 8, 5773--5792 (2000; Zbl 0973.35169) Full Text: DOI References: [1] Farge M., Fluid Dyn. Res. 3 pp 282– (1998) · doi:10.1016/0169-5983(88)90079-2 [2] Foias C., C. R. Acad. Sci., Ser. I: Math. 305 pp 497– (1987) [3] Tian L., Appl. Math. Mech. (in Chinese) 18 pp 1021– (1997) [4] Liu Z., Phys. Lett. A 204 pp 343– (1995) · Zbl 1020.35523 · doi:10.1016/0375-9601(95)00491-K [5] Tian L., Proc. Am. Math. Soc. 126 pp 203– (1998) · Zbl 0889.46023 · doi:10.1090/S0002-9939-98-04014-3 [6] Tian L., Commun. Math. Phys. 201 pp 519– (1999) · Zbl 0940.47028 · doi:10.1007/s002200050567 [7] Tian L., Acta Math. Acad. Sci. Hung. 18 pp 94– (1998) [8] Gomes S. M., SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 33 pp 149– (1996) · Zbl 0845.65048 · doi:10.1137/0733009 [9] Myers M., Physica D 86 pp 396– (1995) · Zbl 0890.58086 · doi:10.1016/0167-2789(95)00076-G [10] Ghidaglia J. M., J. Diff. Eqns. 74 pp 369– (1988) · Zbl 0668.35084 · doi:10.1016/0022-0396(88)90010-1 [11] DOI: 10.1006/jdeq.1994.1071 · Zbl 0805.35114 · doi:10.1006/jdeq.1994.1071 [12] Tian L., Appl. Math. Mech. (in Chinese) 15 pp 571– (1994) · Zbl 0811.35117 · doi:10.1007/BF02450770 [13] Alpert B., SIAM J. Sci. Stat. Comput. 12 pp 158– (1991) · Zbl 0726.65018 · doi:10.1137/0912009 [14] DOI: 10.1002/cpa.3160440202 · Zbl 0722.65022 · doi:10.1002/cpa.3160440202 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.