As President Bush travels across the Pacific this week with his message of conciliation and cooperation, he may be chasing the shadow of Soviet diplomacy.

During his first overseas journey as president, Bush is visiting Japan, China and South Korea. He will attend the funeral Friday of Japan's Emperor Hirohito, his World War II adversary.While in Tokyo, the president also will meet with French President Francois Mitterrand and Middle East leaders, including Egyptian President Hosni Mubarak, Jordan's King Hussein and Israel's President Chaim Herzon, as well as leaders of Brazil, the Netherlands, West Germany, Pakistan, Turkey, Nigeria, Thailand and others.

From Japan, Bush will travel to China, where he spent a year from 1974 to 1975 when he was chief of the U.S. liaison before diplomatic relations were established between China and the United States.

His talks with Chinese leader Deng Xiaoping are considered significant in view of the warming Sino-Soviet relations and a planned visit by Soviet leader Mikhail Gorbachev to Beijing in May.

During his short visit to Seoul, Bush will meet with President Roh Tae Woo and address the South Korean National Assembly.

Brent Scowcroft, Bush's national security adviser, said the trip is "mainly to have some serious discussions with important Asian allies and to make clear the U.S. plans to play an important role in the Pacific."

But the president may be playing a foreign affairs version of catch-up.

Consider Gorbachev's courtship of the Soviet Union's former communist adversary, China, and his new diplomatic campaign in the Middle East.

Foreign Minister Eduard Shevardnadze has stepped into the Middle East quagmire as a mediator, conferring with Egyptian and Israeli officials, thus brightening Soviet hopes of participating in an umbrella international conference for talks between Arabs and Israelis.

The Afghanistan pullout has freed Gorbachev to seek reconciliation on other fronts and he has convinced much of the world that the Soviets have given up their world expansionist goals. He is busy winning friends for his country in the era of "glasnost" and "perestroika" reforms.

So, while Bush reaches out to some old friends, they might be reaching out to some old adversaries.

Clearly, the task of coping with the new Soviet diplomacy may be every bit as formidible as meeting the Soviet military challenge has been. This Asian journey will give some idea of how well Bush is able to respond.