On a new class of completely integrable nonlinear wave equations. I. Infinitely many conservation laws

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Abstract
We point out a class of nonlinear wave equations which admit infinitely many conserved quantities. These equations are characterized by a pair of exact one‐forms. The implication that they are closed gives rise to equations, the characteristics and Riemann invariants of which are readily obtained. The construction of the conservation laws requires the solution of a linear second‐order equation which can be reduced to canonical form using the Riemann invariants. The hodograph transformation results in a similar linear equation. We discuss also the symplectic structure and Bäcklund transformations associated with these equations.

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