Conformal maps and reductions of the Benney equations. (English) Zbl 0936.35184
Summary: We consider Benney’s equations and their reductions to systems with finitely many Riemann invariants. Here we discuss the properties of these equations in more detail, and investigate the relationship between these and Loewner’s theory of conformal mappings of slit domains. A dense family of explicit solutions is constructed.
MSC:
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
| 30C20 | Conformal mappings of special domains |
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