References
- Lannes D. The water waves problem: mathematical analysis and asymptotics. Vol. 188, Mathematical surveys and monographs. Providence: AMS; 2013.
- Didenkulova I, Pelinovsky E. Rogue waves in nonlinear hyperbolic systems (shallow-water framework). Nonlinearity. 2011;24:R1–R18.
- Didenkulova I, Pelinovsky E, Soomere T. Long surface wave dynamics along a convex bottom. J. Geophys. Res. Oceans. 2009;114:C07006.
- Whitham GB. Linear and nonlinear waves. New York (NY): Wiley; 1974.
- Rybkin A, Pelinovsky E, Didenkulova I. Nonlinear wave run-up in bays of arbitrary cross-section: generalization of the Carrier-Greenspan approach. J. Fluid Mech. 2014;748:416–432.
- Polyanin AD, Zaitsev VF. Handbook of nonlinear partial differential equations. 2nd ed. Boca Raton (FL): CRC Press ,Taylor & Francis Group; 2012.
- Kato T. The Cauchy problem for quasi-linear symmetric hyperbolic systems. Arch. Rat. Mech. Anal. 1975;58:181–205.
- Courant R, Lax P. On nonlinear partial differential equations with two independent variables. Commun. Pure Appl. Math. 1949;2:255–273.
- Bressan A. Hyperbolic systems of conservation laws: the one-dimensional Cauchy problem. Oxford: Oxford University Press; 2000.
- Rozhdenstvensky BL, Yanenkov NI. Systems of quasilinear equations and their applications in gas dynamics. Providence: AMS; 1983.
- Dafermos CM. Hyperbolic conservation laws in continuum physics. Berlin: Springer-Verlag; 2010.
- Grimshaw R, Pelinovsky DE. Global existence of small-norm solutions in the reduced Ostrovsky equation. Discr. Contin. Dynam. Syst. A. 2014;34:557–566.
- Liu Y, Pelinovsky D, Sakovich A. Wave breaking in the Ostrovsky-Hunter equation. SIAM J. Math. Anal. 2010;42:1967–1985.
- Imanaliev MI, Ved YuA. On a first-order partial differential equation with an integral coefficient. Differ. Eqs. 1989;25:465–477. Russian.
- Imanaliev MI, Alekseenko SN. On the theory of nonlinear equation with a differential operator of the full time derivative type. Dokl. Akad. Nauk. 1993;329:543–546. Russian.
- Alekseenko SN. A basic scheme to inverstigate two first-order quasi-linear partial differential equations. Analytical and approximate methods. Aachen: Shaker Verlag; 2003. pp. 1–14.
- Imanaliev MI, Alekseenko S. On the existence of smooth bounded solution for the system of two nonlinear first-order partial differential equations. Dokl. Akad. Nauk. 2001;379:16–21.
- Kellogg RB. Uniqueness in the Schauder fixed point theorem. Proc. AMS. 1976;60:207–210.